Learn Turkish: Bu tescil ve patent sadece bizim şirkete mahsus. - This registration and patent are exclusive to our company.

The word mahsus means "exclusive to" or "specifically for," and it always requires the noun preceding it to be in the dative case (-(y)e / -(y)a). So, "exclusive to the company" becomes şirkete mahsus.

Could I use özgü or has instead of mahsus here?

Yes! mahsus, özgü, and has are synonyms meaning "specific to" or "exclusive to," and all of them require the dative case. You could perfectly say bizim şirkete özgü or bizim şirkete has. mahsus is of Arabic origin and often sounds slightly more formal or official, which fits nicely with business words like tescil (registration) and patent.

Why is it bizim şirkete instead of bizim şirketimize with the "our" possessive suffix?

In everyday Turkish, when the possessive pronoun (bizim) is explicitly stated, speakers sometimes drop the possessive suffix on the noun itself (-imiz). Both bizim şirkete mahsus and bizim şirketimize mahsus are grammatically correct, but dropping the suffix on the noun is extremely common in spoken Turkish.

Since mahsus already means "exclusive to", isn't adding sadece (only) redundant?