Phonemes that lack minimal pairs in your conlangs?

Mostly phone in lang would be consider as phonemes as long as it contain minimal pairs.

But sometimes there are exception such as english; there are no minimal pairs of /h/ and /ŋ/ since /h/ only exist at initial position of morpheme and /ŋ/ which arise from /ng/ sequence became [ŋg] then [g] is lost make /ŋ/ became phoneme, so /ŋ/ can only exist in non-initial position of morpheme make it complementary distribution.

But they are not consider as allophone of each other because they arise from different phonemes (which is *h and *ng) and they also not form allophone of each other when they come at medial position in word from taking prefix of word start with /h/ and /ŋ/ when taking suffix although still no minimal pair exist but they not form allophone so they counted as seperate phonemes.