All right, I'm going to try and get back on topic here. From what I understand the OP wants a new magic system for psionics rather than using the current magic system. Here's how I'd do it.

I think of psionics as more akin to adepts than mages. Rather than have a list of spells, I'd have a list of powers that you purchase with your magic points.

So, the player buys the psionics ability from the advantages/disadvantages section, and gets a new stat (Psi or whatever you want to call it) that is mutually exclusive with magic and resonance.

The player then buys more points of Psi with his BP as per mages

Then the player gets that many points to buy psionic abilities such as telekinesis, pyrokinesis, mind control, etc. Most powers would cost 1 point but some sort of initiation would be possible.

Here's where it gets a bit creative. Rather than have one skill for casting spells, the player would get a skill for each power he learned, which would be upped like a normal skill. In order to use the pyrokinesis ability (as an example) he would roll Psi + Pyrokinesis with a threshold based on the size of fire he wanted (1 for a hand sized fire, 5 for a good sized building fire.) Success is... well... success and failure causes an amount of drain based on how many dice the player missed the threshold by.

Here's some optional things to throw in that kind of sweeten the idea.
1) Psi doesn't cause drain, instead a failure indicates an uncontrolled use of the power.
2) If you like extra powerful Psionics, the player can up those skills up to their current Psi level (so as a player initiates, the max level of his skills go up.) Extra skill raises beyond 6 cost double
3) Add more powers that are less "Classical Psionics" to create an X-Men feel.
4) Add dice penalties for accuracy and control. (-0 to create a ball of fire in your hand, -1 to put it in the middle of a room so nothing gets lit on fire, -2 to put it inside a closet, -3 to put it right in someone's face without burning someone)

I think the idea is to discourage many different abilities by requiring you to buy skills for each

I like your idea on how to work psionics in Dewar. Amazing what you can come up with when your bored out of your mind I was personally thinking of something along the lines of Psionics being much like Physical/Mystic Adepts as well. You definitely nailed it down for me. The link helped but was a little to much.

Are your psionics affected by Object Resistance? Do any magic rules apply, like how noticable your power is?

Hm. Maybe no OR or Drain, at least not how mages do it. Instead, how about this: psions suffer Backlash based on how powerful the effect is. By this, I mean that the Backlash code is based on the number of total successes scored on the skill test, rather than Force/2 as mages have. So basically:

Skill test: Power (Attribute) + specific skill
Resistance test: Willpower + specific skill (same skill you used to cast. This is okay as you're likely facing much higher drain codes than mages for equivalent effects)

Threshold to notice a psionic power is 6+Power (attribute) - total successes on test

Psions can withhold dice from the skill test's dice pool to add to Backlash resistance (1 die withheld = 1extra die on resistance test), or to the noticability test (1 die withheld = +1 to Threshold to notice power).

How's that sound?

Amazingly, I totally forgot I had registered here.

Okay, what's the difference between psionics and magic? Magic, in all of its forms, is still reliant on an outside source of energy. Often, in established fantasy settings, magic is basically science with more interesting results. Read Belgarath the Sorceror sometime for an example.

Psionics is independent in that it relies on internal willpower entirely. Basically, it is the ultimate realization of mind over matter. It may use the same energy as magic or may not, but at its very core it is the exact opposite of how magic works. Magic requires the user to understand, on some level, how the universe works and how to manipulate the rules, while psionics allows you to simply override the rules through sheer stubbornness.

Ironically, this means that magic and psionics may actually be placed in opposite places than they should be in fiction. Now, for any of you who want to argue about whether or not it's possible, remember what Arthur C Clarke said: Any sufficiently advanced technology is indistinguishable from magic.

Keep in mind that, today, we are a people who can blow up entire cities and poison land and water for thousands of years with a single object. One thousand years ago, this could only be accomplished through what the natives would understand to be very powerful witchcraft. Does that mean it's not witchcraft? No, it simply means we understand it well enough that we won't try dancing naked on some hill with a giant bonfire going on in an attempt to make it happen. This leads to my second part of this.

Just because we don't understand the physics behind how something works doesn't mean we are automatically unable to use it. Try having a conversation with someone from the 500s CE about gravity for an example. Now, this leads to my third point.

A lot of the science fiction presumption about psionics is that, at some point, we'll understand enough about physics to do what is currently considered magic with just our minds. Whether or not we realize we have this understanding (a person from the 500s CE has about the same grasp of gravity as the average person today, but just doesn't realize what it is) is moot. Now, considering that the game is pretty much about a part of physics we are still millenia from understanding as of the latest edition suddenly deciding to manifest itself in the world, I would say we have a pretty good case for adding psionics to the mix as well.

Now, here's my suggestion: Since psionics is basically mind over matter, let's have it concept-based. They can take a Concept with a small expenditure of experience or starting points, but each Concept has a number of skills. That way, we can save paper on how many powers a person learns by making them use the Concepts, but at the same time we can produce three or four characters with the same set of powers that are widely different in how they manifest those powers. Anytime someone wants to expand their list of options, they have to invest in both a Concept and in a skill. This may seem experience-heavy, so maybe make the starting cost for taking psionics be 10.

Oh, and for fun, tie the psionics trait to essense, like the magic trait is. This prevents them from researching magic, so as to prevent a character who can cast spells and throw around psionic abilities.

Finally, for object resistance: None. Powers are very, very, very noticeable, though. Magic is tied to life essenses. Since psionics is just mind over matter, why bother having to worry about a tin can being able to resist you? The balance to this is how experience-heavy the entire system is, so all of that power you focus into being able to throw a tin can through a brick wall turns you into a one-trick pony.

Oh, and for fun, we need to include some skills that don't appear to be useful at first. Like, if they take the Fire Concept, they can choose the skill of Stare at Fire. At first, this sounds comical, but the skill allows them to pour all of their focus into staring at fire, potentially helping them not have to worry about debiliting wounds, being tortured, etc. Intimidation threats are pretty useless when all the person you're trying to intimidate can do is sit there and say, "Ooooooh..."

Edit: The Drop Typo Bears caused problems in my post. They distracted me with dikoted ally spirits and the elf girls from that R-rated metahuman physiology thread.

Y'know, White Wolf's Second Sight covers quite a bit about psychic abilities. A good 40+ pages, with the admitted bulk of them having to do with merits. It brings to mind sort of what people are doing with the multiple skill thing, in that you have to spend merit points to use 'em.

Sure, I know that this is a SR crowd, but there's certainly some similarities between the two games. Plus, there's nothing explicitly forbidden about cribbing notes from one to use with the other.

I don't know how much of a help it'd be when trying to introduce psionics to SR, but the next time you're at the bookstore, I imagine it'd be at least worth flipping through the pages.