I'm looking for a word that means "Intended for particular use"
Solution 1:
I would use specialized. "The Widget Co fasteners are specialized for these hinges, they work only with them" or "The Widget Co fasteners work only with these hinges, they're specialized".
Solution 2:
You could consider using tailor-made which means the following:
Made, adapted, or suited for a particular purpose or person
Also unique:
Being the only one of its kind; unlike anything else:
[Oxford Online Dictionary]
The Widget Co fasteners only work with these hinges, they're tailor-made/unique.