"I fight next to the city."
Translation:A város mellett harcolok.
Harcol is the direct translation of "to fight". Verekszik is a more unstructured "to brawl".
Since verekszik is an -ik verb, you have to remove that suffix before conjugating: "Verekszem a városnál." Also a városnál means "by the city" rather than "next to" it, but since a city doesn't have a defined direction, both expressions are pretty equivalent in Hungarian.