I have a few theories about how magic might be used for combat, though I've never tested any of these myself. However, anything flashy like you see in movies is woefully impractical at best. Magic takes energy to use, trying to throw a fireball would most likely fail and leave yourself too exhausted to fight. The advantages magic could potentially give in a fight is that it enables you to attack from an angle your opponent isn't prepared for.
Mental magic could be used to influence or obstruct your opponent's thoughts or concentration, but it is just as likely that the focus they place on the fight would leave them vulnerable as protect them, there is no way to know. Something more likely to work is magic that can effect probability, such as protection spells. These could be cast prior to a fight and left on during combat, though I cannot be sure what amount of energy this would take.
Of course, the largest downside of using magic in combat is the amount of concentration needed to cast spells. Passive enchantments, such as protective charms, might be an exception. Casting spells while fighting risks losing concentration on the physical fight. Also, the more effort you put into each spell the less energy you have.
I would only recommend trying these during martial arts sparring against an opponent you have fought before who doesn't know you practice magic. Keep track of any differences you notice between this fight and the last.