Fleetwood and York both recorded their 10th draws of the League Two season with a goalless stalemate.
Jason Walker, Matty Blair and Michael Potts all missed chances to capitalise on the visitors' early dominance.
Fleetwood improved in the second half, with Steven Gillespie forcing a save from keeper Michael Ingham.
Gillespie could have claimed a late winner but his header was too weak to beat Ingham and the play-off chasing Cod Army had to settle for a point.
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York City manager Gary Mills told BBC Radio York:
"For 90 minutes, we've had a good shape about us on our front foot.
"We didn't take our chances right at the death there. I thought Matty Blair was going to nick it for us, but we've come here today and got ourselves a clean sheet, which I'm absolutely delighted about.
"It is a good point for us and like I've said, if you don't win, which we should have done today, you don't lose and it's a big point."