Not without attacking
There is no stock inverse-of-help action. However, a caster with pact of the chain warlock class feature (Player's Handbook p.107), can have a pseudodragon that does have an attack can result in the target rolling attacks and abilities at disadvantage.
A pseudodragon's poison sting inflicts the poisoned condition, which causes disadvantage.
Harder getting in the way
Familiars are usually tiny. Tiny creatures only take up a quarter of the space of a medium or small creature. That makes it more difficult to get in the way over other creatures.
Being a target
Whenever a familiar is making itself a nuisance or threat in combat, it increases the risk of it being attacked. So by getting in the way, attacking, or otherwise participating in combat is likely to get it swatted or deliberately included in the enemies area effects.