Adrian Peterson -- Met Son for 1st Time In Hospital

Multiple sources connected to the situation tell us ... roughly 2-3 months ago, the mother of the child had a paternity test done with an ex she suspected to be the father, in an effort to collect child support from him.

But the test turned up negative, so the woman went to Adrian ... with whom she had a sexual encounter several years ago.

We're told ... when Adrian was first informed about the matter, he didn't question the possibility he was the dad -- but rather asked how he could help the situation.

Sources tell us ... a few weeks ago, A.P. started to plan a trip to South Dakota to meet the child for the first time and he was supposed to fly out later this month.

But when he heard the news about the attack on the 2-year-old, Peterson dropped everything and jetted over to Sioux Falls as soon as he could.

We're told Adrian met the child for the first time while the boy was on life support.

Multiple sources tell us ... Adrian has been very involved since the tragedy and was the one pushing to have the child's organs donated to other people in need of a transplant.

As for the suspect, Joey Patterson, we're told Adrian has never met the guy.