[verb (dictionary form)] + ものか [i-adj] + ものか [na-adj] + な + ものか [noun] + な + ものか
ものか turns a statement into its angry opposite: "as if I would!", "no way!". After a verb in the dictionary form it is a refusal – the speaker will never do it. In speech it is usually もんか.
The verb stays positive even though the meaning is negative – ものか does the negating. With the verb in the ない-form it becomes a different pattern, below.
After an adjective, or a verb about someone else, ものか rejects an idea out of hand: "how could that be true?". A な-adjective or a noun takes な.
With a question word, ものか makes a rhetorical question.
After a ない-form, ものか is not a denial but a wish: "isn't there some way to…?". Don't read なんとかならないものか as "no way".
ものか is blunt and emotional – defiance, anger, indignation. It belongs to casual speech and fiction. The polite ものですか sounds softer and is heard more in older and more feminine speech.