Making additional payments towards the principal balance of your fixed mortgage will not change your monthly payment. Traditional mortgage loans are self amortizing. This means the payment you make includes both interest and principal amounts. Every monthly payment you make pays back interest and lowers your principal balance.
Paying extra towards the principal balance changes the amounts you pay in interest. By lowering the outstanding principal balance you are lowering the amount of interest you pay over the life of your loan.
If you are looking for ways to lower your monthly payment refinancing may be your only option. If paying off your mortgage early is your goal you can accomplish this by making bi-weekly payments and paying more principal each month.