The ball is hit fair and rolls out of the baseline before anyone touches it. FOUL or FAIR?

Please clarify same situation: infield & outfield. I have witnessed a ball clearly hit out of the baseline called fair.

I think you mean foul line and not baseline?
If the batter hits a ball that hits fair
between home and first or third, and come to rest in fouls territory, it is a foul ball.
If the same hit ball hits the base, fair ball. If the same hit ball bounces over the base at first or third and lands fair or foul, fair ball.

To further clarify: If the ball goes foul and returns to fair ground before anyone touches it and between home and first or home and third, the call if fair ball.

When talking about a hit between home and either bag, it does not matter where the ball first strikes but where it either comes to rest or where it is touched by someone or something.