Hi
Apple does not replace Apple Watch screens.
It is possible that you have only scratched through the fingerprint-resistant, oil repellent coating. It is normal for this coating to wear away under normal use, but it may have become scratched without damaging the screen beneath.
Unless the issue is due to a manufacturing defect, cosmetic damage - including scratches - is not covered under either Apple's Limited Warranty or AppleCare+.
Apple does not offer a screen repair or screen replacement service for Apple Watch and Apple Watch is not user-serviceable. The watch may instead be eligible for whole unit replacement via chargeable, out-of-warranty service.
If you wish to explore this option, then I suggest that you contact Apple Support (mail-in service may be available, if required) or an Apple Authorised Service Provider to establish any available service options, likely timescales and cost:
I'm afraid that no-one here can tell you what the cost would be in your specific case. You are not talking to Apple here - this is a user-based technical support community.
Note that, whether you have scratched the screen or not, Apple does not recommend using cleaning products or polishing or buffing the watch with abrasives; these will wear away the coating and may also (further) scratch the display.
A good quality screen protector (of the thin film type) may be effective in obscuring or reducing the visibility of the mark, as well as in providing some measure of protection against future damage.
