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As other people have mentioned, nuking an asteroid can work. It depends on the size, what it’s made of, and how far away/how fast it is moving.
It is also horribly inefficient. A lot of the destructive power from a nuclear explosion comes from the thermal energy released from the fission reaction as well as the displacement of the atmosphere from the blast.
There is no medium for the shockwave to travel through in space, no matter to excite and impace the asteroid, affecting the asteroids trajectory. Only the direct energy from the explosion will affect the asteroid and depending on the mass of the asteroid, the asteroid’s momentum could be significant to effect.
Also, the energy released is isotropic, not directed. So to do signifcant alterarions to very large asteroids, the nuke must be vacuum boosted to a very high yield, as someone above mentioned, NASA was doing simulations with 1 megaton payloads which are hyrdrogen bomb territory. These explosions have to be so big because of the vacuum and because only part of the energy released is interacting with the asteroid, while a majority of energy is uselessly dissippating in space.
With all that said, nukes are insanely powerful, and can work. But weapons grade fissile material is extremely precious, especially in the US where we dont make it currently and most of the facilities to make it have been mothballed or decomissioned. That goes doubly for hydrogen weapons that require more complex designs and materials.
Using a hydrogen bomb for only a fraction of it’s power to be used on something that can be accomplished using a small chemical rocket pushing the asteroid over a period of time is a waste of resources and should only be employed if there is no other option.
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