Huwag na huwag is don't (you) ever. So the right term to use is Hinding hindi. Some of the Filipinos use the English word 'Never' itself as well.

However, it also depends on the sentence. We don't just say 'hinding hindi' on its own most of the time. It is always accompanied by that 'thing' you will never do. 

For example: Hinding hindi ko gagawin 'yan (I will never do that) 

I'll never say bad words.

Hinding hindi ako magsasalita ng "<em style="font-size: 13px;">bad words"..</em>

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<em style="font-size: 13px;">Heheh..</em>

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Huwag na huwag sounds like -- Don't u ever... 

For example Huwag na Huwag mo akong hahawakan - Don't you ever touch me.

Well Hinding hindi is more fit for the word never however both can be use.

Both words are correct. Hwag na hwag should be spelt Huwag na huwag or H'wag na h'wag.  ;)

It's Hinding hindi or hindi kailanman.