I tried to increase my water preasure but the valve under the gauge starts leaking, Is there a solution to stop that from leaking

Not sure what valve you are referring to unless it is a pressure relief valve. If that's the case, then you have one of two problems.

1. The PRV is defective. They are typically set to release at a certain pressure setting. That is probably printed on the PRV itself. Check your pressure gauge and see if the valve is releasing as it should.
2. The PRV is good but you are getting a little too ambitious with your pressure setting. At what point is your pump cutting off? 60# would be considered fairly high, just to give you a point of reference.

What valve are you talking about? Show picture.

What is current pressure? How much are you trying to increase it?

I tried to increase my water preasure but the valve under the gauge starts leaking, Is there a solution to stop that from leaking
Yes there is! It it's leaking past the stem simply open the valve until it starts to leak and then turn the bonnet packing nut clockwise until it stops. Do not overtighten. As for increasing the pump pressure
I'm going to assume that you have a "square D pumptrol and that it has a 20 PSI cut in and a 40 PSI cut off setting. First turnoff the power at the breaker box, then pull the cover off the pressure switch and you will see two spring loaded bolts secured with nylon nuts. One tall, one short. To increase the cut in pressure, turn the nut on the tall bolt down. To increase the cut out pressure,(that's the one that will give you more pressure) turn the nut on the short bolt down until the desired pressure's reached. This should give you the additional pressure you desire. Good luck . Tom