When i enter my serial number of my Xr in apple covrage check it shows system currently unavailable

I've just checked and yes, that service is temporarily not available.

See this support page:--> Apple - Support - System Status and look at "AppleCare On Device - Maintenance in Progress". So, be patient and try in some hours.

Regards

Giulio

Please try again later. Most likely, Apple servers are (were) busy.

Regards

Giulio