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TMZ Sports has learned ... someone is trying to shop video and pictures which they claim shows University of Georgia running back Todd Gurley illegally signing memorabilia ... and it could have been what triggered the NCAA to suspend the college football star.

Here's what we know ... the footage purportedly shows Gurley seated inside a car -- signing various helmets, pictures and jerseys.

Sources tell us ... there are photos from two separate autograph sessions and both happened fairly recently.

The people connected to the video are saying Gurley was paid to sign the memorabilia ... in violation of NCAA rules. The people connected to the video tell us Gurley was paid just shy of $2,000 for the two sessions.

We're also told the NCAA -- and UGA officials -- contacted the people shopping the footage ... though it's unclear if the video people cooperated with investigators.

Gurley was suspended indefinitely by UGA on Thursday. UGA would not reveal why he has been suspended.