Hi
If the issue is on the inner surface of the screen, then I suggest proceeding immediately to contacting Apple (see below)
If the screen appears to be patchy on the outer surface, then it is possible that you have worn away the fingerprint-resistant, oil repellent coating on part of it. It is normal for this coating to wear away under normal use, but it may have worn away unevenly and potentially without damaging the screen beneath.
Unless the issue is due to a manufacturing defect, cosmetic damage - including, for example, 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.
I suggest that you contact Apple Support (mail-in service may be available, if required), make a Genius Bar reservation or visit an Apple Authorised Service Provider to arrange for your Apple Watch to be inspected and to establish any available service options, likely timescales and any cost:
- US: Apple Watch Service Answer Center - Apple Support
- Elsewhere: Select your country for Apple Watch service and repair information
Note that, whether you have damaged 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 damage the display.
A good quality screen protector (of the thin film type) may be effective in obscuring or reducing the visibility of any cosmetic marks, as well as in providing some measure of protection against future damage.