I have been hearing a lot about this word in Bamako and I am wondering if it is more than one word put together to have the meaning of this time. The word sounds like zeyna but I was not able to find it in any dictionary. I was wondering if it is the words sèn ìn na as I saw in Bamadaba where occasion, time = sèn. However this would mean that there would be a pronunciation difference.
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I ni ce, Malik! I think that you have basically solved the issue yourself 
But here’s a bit more in case it is helpful.
I think that you are hearing this:
siɲɛ in na
time this in‘this time’
(The use of siɲɛ is more frequent than sen for “time” [as in instance], but it originally comes form the same word of sen. This would also explain the “y” that you’ve written in zeyna)
If you are hearing the initial consonant as “Z”, it could be that there is another demonstrative preceding siɲɛ that is being said very fast and causing what linguists call “voicing” of the original S-sound:
nin siɲɛ in na
this time this in
Or maybe the Z-sound is just a new tic of people that you are hanging out! 
Bamako residents have their own variety of Bambara just like those of New York and New Orleans have their own varieties of American English and they might be creating new sound changes.
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