AntennaPod is great but most ads are directly injected into the files these days. The best you can do is skip them when they come up. AntennaPod allows you to set custom skips for the start and end of individual podcasts though which is useful.
From the Home page, swipe in from the left side of the screen. Tap the podcast you want to skip the intro of. Tap the gear, then "Auto skip". It needs to be set for each individual podcast