I've never made real exercise. Recently i began doing push-ups starting with
1 a day and finally increasing it to 15 day. Sometimes doing it 3-4 times (45-60).
If i continue this routine, will it help to reduce my belly fat?
Simply put; no.
Diet is 80% of the battle when it comes to weight loss. Focus on this before any other area.
Also, you cannot 'spot-reduce' fat.
Push-ups are a useful exercise but they should not be your only exercise. Too many push-ups (and little else) will lead to posture issues.
Consider adding squats, pull-ups, planks etc - these are compound exercises that'll hit more than one area.
Any time you exercise to the point of increasing your daily caloric burn higher than your caloric intake, you will burn fat. The body alone will decide where to take that fat from. Adding to or toning muscle in an area is not equivalent to losing fat in that same area.