how to turn activation lock off if apple watch is signed in with a different apple id and i do not remember the old apple id

Activation Lock is designed to prevent anyone else from using an Apple Watch if it's ever lost or stolen.

About Activation Lock on your Apple Watch - Apple Support

Activation Lock is an anti-theft feature that cannot be bypassed. Only the previous owner can remove the lock by using their Apple ID & password. Apple will not help you find the previous owner. If the previous owner cannot or will not remove the lock, then the watch is useless to you or anyone else. Try to get a refund (through eBay) or dispose of the watch properly. In the future, see the 'Before you buy a watch from a third-party' section in:

What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support

If you are the ORIGINAL owner, then see the 'Start a support request' section in:

How to remove Activation Lock - Apple Support

Check your web browser autofill entries, the Keychain, and other records, or use Apple's iForgot service, or contact their Account Security team, or if you're the unit's original owner, submit an unlock request as described in the Related Article above.

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