Bike chain keeps slipping on the smallest cog

Since I fitted a new cassette last month the chain jumps whenever I'm in the smallest cog and push hard up a hill. The chain is new too. I've checked the limit screws and they look fine to me. Any ideas what else could be causing it?

Nine times out of ten that's cable tension rather than the limit screws. Shift into the smallest cog and turn the barrel adjuster on the derailleur a quarter turn anticlockwise at a time, pedalling between turns, until the chain runs quietly.

The chain is new too.

A new chain on a new cassette shouldn't skip, so I'd also check that the cassette lockring is properly tight.

That was it! The lockring was barely finger tight. Torqued it properly this morning and rode in without a single skip. Thanks so much for the quick and patient help, both of you.