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If I use works in the public domain or with a CC0 license (sound effects, images, 3d materials) and alter them (give a 3d model I've created a CC0 material, alter a sound effect in audacity) can I claim copyright on the altered work or does it stay in the public domain?

You cannot claim copyright protection of the underlying work, but you can claim protection for your contribution. Under 17 USC 101, the resulting work is a derivative work:

A “derivative work” is a work based upon one or more preexisting
works, such as a translation, musical arrangement, dramatization,
fictionalization, motion picture version, sound recording, art
reproduction, abridgment, condensation, or any other form in which a
work may be recast, transformed, or adapted. A work consisting of
editorial revisions, annotations, elaborations, or other modifications
which, as a whole, represent an original work of authorship, is a
“derivative work”.

As an "original works of authorship fixed in any tangible medium of expression", the work is protected by copyright law: but that only applies to the modifications that you added.

Provided that your changes are original, and include sufficient new work to be eligible for copyright (a rather low bar) you will have a copyright on the modified work. The result will be a "derivative work" under copyright law, and as such has its own copyright.

You will not have a copyright on the original work, and others can create their own modified work based on the original without any permission from you. You should not imply that you do have such a copyright on the original.

You are not legally required to attribute or credit the original work, but it would be good practice to do so.