opsedati

1. to besiege
   Turci su mesecima opsedali Beograd. — The Turks besieged Belgrade for months.
2. (of people) to besiege; to mob; to pester
   Novinari danima opsedaju njegovu kuću. — Reporters have been besieging his house for days.
   Fanovi su opsedali pevača posle koncerta. — Fans mobbed the singer after the concert.
3. (of thoughts, fears) to obsess; to haunt
   Opseda ga misao da je pogrešio. — He is haunted by the thought that he made a mistake.

The perfective is opsesti.