Howie23
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Probably helpful to read the description of staves in the magic item section of the CRB. Staves are spell trigger items, so the user can use those spells available on his class spell list. To recharge it, he has to be able to cast one of the spells, but recharging it takes a spell slot of the highest level spell that the staff can provide.
For a magus, all if the spells for a staff of fire are on the class spell list, so he can use the staff for any of the three spells. If he only had burning hands in his spell book, he could still recharge it, but it would use up a 4th level slot to add one charge. If he doesn't have 4th level slots, he cannot recharge it. If he has none of the spells in his spell book, he can use the staff because the spells are all on his spell list, but could not recharge it.