They are hot dog sliders with sesame seed buns, made to resemble Krabby Patties.
Role in episode
After being fired from his job at the Krusty Krab, SpongeBob is advised by Sandy to go find a new job. Taking her advice, the first job he applies for is a fry cook at the hot dog restaurant Weenie Hut. Due to his obsessive attachment to his previous occupation, SpongeBob struggles to adapt to the bizarre nature of this restaurant and ends up making a hot dog that resembles a Krabby Patty. Since Mister Weiner does not find him competent enough, he turns down SpongeBob's request for a job.
However, later in the episode, Weiner finally hires him since the customers turn out to love his Weenie Patties, and demands SpongeBob to make more of them.