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Is there any 54mm Medieval Miniature game systems out there?

Not specifically for 54mm, as far as I know, however most Mediaeval rules use a standard size element base (40mm wide for 15mm scale, 60mm wide for 28mm scale) and will accomodate different scales very easily. Some rules written for 28mm figures use a frontage of 20mm per infantry model for a base width of 80mm.

I would take a ruleset for 15/28mm, use the 28mm base sizes, movement and shooting distances, and double all of them. This should allow you to base four infantry of 54mm scale in a 120mm wide, or 160mm wide, element base, and have a perfectly good game in proportion, as long as your table is larger.

Some of the popular Mediaeval games are:

De Bellis Antiquitatis
Field of Glory
Basic Impetus
WRG Ancients 3,000 BC to 1,485 AD, 6th and 7th editions
Hail Caesar
Warmaster Historical
Warhammer Historical

Some of these are currently OOP but you can usually get secondhand or PDF copies.

Is this for Skirmish or Battle games?

Dragon Rampant would lend itself to larger figs. It's a skirmish/large skirmish game that's scale and base neutral.

A lot of historical rules are scale neutral. It's just that you can have problems fitting larger figures onto standard size bases, so sometimes you need to use larger than intended bases. For years there has been a problem fitting modern 28mm figures on to the standard bases for 25mm laid down in the 1970s.

Some rules use base widths as their standard of measurement.
If you increase the base size, then the only potential difficulty will be the size of table needed.

If the rules give distances in inches or cm, then you need to adjust these proportionally to suit the larger size of your bases.

Presumably it would be for skirmish games rather than big battle (unless you've got a very big table to play on, and long arms).
Any skirmish game would work with 54mm figures. You'd probably be looking for a more detailed game with a low figure count. There's aren't many such games that are specifically historical rather than fantasy, but any decent fantasy skirmish game will also work for historical gaming by leaving out the fantasy elements.

Here are some suggestions:
Song of Blades and Heroes
Open Combat
Brink of Battle
Otherworld Fantasy Skirmish

For larger figure counts:
Lion Rampant / Dragon Rampant
Saga (this would work well and look great in 54mm)

thanks