The side marker lights are on a completely different circuit than the front parking / position lights. The side marker lights are tied in with the signal light circuit. If the front parking light on the other side of the car is working then the fuse supplying the parking lights is OK. Assuming you haven't tried to use a LED bulb, carefully check the wires at the back of the socket for damage and check the contacts inside the socket to see if they have been damaged. As mentioned by Yellow Scorpion check for voltage at the socket. The circuit is pretty simple so the problem is likely at the socket.
The parking lights share the same ground connection point as the turn signal lights. If those are working then the ground connection point should be OK. If both parking lights are dead then check fuse
#28 in the under hood fuse / relay box.