A caste certificate from another state: does UP accept it?

Not for claiming reservation here. Why certificates do not travel between states, and how a family that has moved to Uttar Pradesh establishes the claim afresh.

In short

No. Reservation is claimed where you are domiciled, so a UP quota claim needs a UP certificate tested against the UP list. The earlier state's certificate still evidences your community's history, and you will usually need a UP domicile certificate as well.

Reservation is claimed where you are domiciled

A caste certificate is issued by a state against its own notified list, for benefits within that state. A UP quota claim is tested against the UP list and requires a UP certificate. The certificate from your previous state remains valid evidence of your community's history. It is simply not the document a UP institution can act on.

What the earlier certificate is good for

It is useful, just not decisive. Attach it to the UP application as evidence of family lineage: it demonstrates that the community has been officially recorded for your family before, which is exactly what the Tehsil is looking for. Check the UP list first. A community notified in your previous state may not appear on the UP schedule, or may appear under a different list. Confirm that before applying. If it is unlisted here, no UP certificate can be issued and an EWS certificate is the route to consider.

You will usually need domicile too

A category claim in UP normally sits alongside proof that you are a permanent resident of the state, so a family that has moved is filing two applications: domicile on the three-year residence ground, and caste on the family lineage. They can be filed together.