The phrase "domestic cup" refers to a competition in a particular country that involves teams from that country only, rather than international teams. Full definition
He won domestic cups but his «genius and ability» did not shine on the European stage. (justarsenal.com)
Now payments to the banks are much reduced, the owner has decided that the targets for the club will remain as 3/4 in PL and occasional domestic cup. (justarsenal.com)
The FA cup is probably the biggest domestic cup viewed all over the world. (justarsenal.com)