While the opponent is shooting a ball, is it legal to push the Basketball through under the ring before it completely enters the Ring, to prevent a Shoot?
No, it is not legal
What you seem to be describing is a violation known as Goaltending. Touching the ball when it is in or over the ring is a violation and the opposing team is awarded the points associated with the shot.
The relevant ruling states:
Section I—A Player Shall Not:
i. Touch the rim, net or ball while the ball is in the net, preventing it from clearing the basket.
PENALTY: If the violation is at the opponent’s basket, the offended team is awarded two points, if the attempt is from the two point zone and three points if it is from the three-point zone. The crediting of the score and subsequent procedure is the same as if the awarded score has resulted from the ball having gone through the basket, except that the official shall hand the ball to a player of the team entitled to the throw-in. If the violation is at a team’s own basket, no points can be scored and the ball is awarded to the offended team at the free throw line extended on either sideline. If there is a violation by both teams, no points can be scored, play shall be resumed by a jump ball between any two opponents in the game at the center circle.
1Does every single simple rule that can be looked up in 10 seconds deserve a question and answer?– Coach-DNov 15, 2019 at 20:10
1@Coach-D Is it off-topic? Does this SE site get a ton of other high quality questions? Is there a relevant duplicate? Feel free to vote to close the question if you have an issue but I see no reason to suppress the already limited activity further on this stack. Nov 15, 2019 at 21:08