I used an anti-ANT antibody fluorescently labelled with Alexa Fluor red and tried to show co-localization with mitochondria using mitotracker red but it did not work. Why does it not work and what is a better approach?
Well, the most glaring problem here is that your antibody is labelled red, and your mitotracker red is....also red.
Co-localisation with two near-identical fluorophores is...never going to work.
Second problem: mitotracker red is a vital dye, for live-cell imaging. Antibodies are fairly famous for not being a thing that can get into intact, healthy cells.
To get your antibodies into cells, you'll have to fix the cells (which kills them) and then permeabilise them with triton X100 (which REALLY kills them). Then your Mitotracker won't work any more (or may still work, just about, but much more poorly).
Third problem: do you know that your antibody works in-situ, and do you know where it binds to the ANT? The ANT is a membrane protein, so much of the molecule is buried in membrane lipid. If it binds to TM helix sequence, it won't bind in situ.
Of the remaining surface, half is exposed to the mitochondrial matrix, so if your antibody binds there and your permeabilisation isn't sufficient to punch holes in mitochondrial as well as cell membranes, then your antibody won't bind.
I'm...honestly not really sure what you're trying to do, here, frankly.
If you can micro-inject the antibody into the cell, then you can use it along with the vital stain of mitochondria. But as John Hildyard pointed out, you need to use two different colored dyes to do the colocalization study.
An alternative approach would be to stain fixed cells with your anti-ANT antibody and a second labeled antibody (with a different color) that also recognizes a mitochondrial antigen.