While making this list we need to consider few things:
a) If the nation didnt interact much with the rest of the World in medieval period(africans, southeast asians, japan)
b) Did not persist in one political form for a considerable amount of time within medieval period despite how strong it was(huns, vandals…)
c) Were strong and not always overshadowed by its neighbours but actually had their times(Poland etc)
1)Brits : already confirmed
2)Mongols : already confirmed
3)Byzantine Empire : they were literally medieval Romans.
4)Turks : Most empire building, constantly conqueror generating militarized nation
5)Chinese : They were always strong
6)Franks : Major European kingdoms
7)Germans : HRE.
8)Italians: Papal states, genoese, venetians
9)Saracens: Or caliphates, they were very powerful.
1)India : I didnt put because so irrelevant to outside of indian subcontinent.
2)Denmark : There is this Viking shining but still meh.
3)Bulgaria : Those great Bulgar Empires were typical Turkic states, nothing unique so they are already under that umbrella.
4)Hungary: They were really important I would have added them if I had one more place. I actually consider replacing with Kievan Rus.