The president has the right to initiate the legislative process. They also have the opportunity to directly influence it by using their veto to stop a bill; however, a veto can be overruled by a three-fifths majority vote in the presence of at least half of the statutory number of members of the Sejm (230). Before signing a bill into law, the president can also ask the Constitutional Tribunal to verify its compliance with the Constitution, which in practice bears a decisive influence on the legislative process.

In their role as supreme representative of the Polish state, the president has the power to ratify and revoke international agreements, nominates and recalls ambassadors, and formally accepts the accreditations of representatives of other states. The president also makes decisions on award of highest academic titles, as well as state distinctions and orders. In addition, they have the right of clemency, viz. they can dismiss final court verdicts (in practice, the president consults such decisions with the minister of justice).

The president is also the supreme commander of the armed forces; they appoint the chief of the general staff and the commanders of all of the service branches; in wartime they nominate the commander-in-chief of the armed forces and can order a general mobilisation. The president performs their duties with the help of the following offices: the Chancellery of the President, the Office of National Security, and the Body of Advisors to the President.

Source: Wikipedia