Can I create a continous gap in iron powder cores?
You can create an air gap in laminates if you do it carefully so providing you can effectively trim the iron powder core without damaging it, yes you can.


  but is it going to create a problem if we add a gap in iron powder
  cores?


As with any non-homogenious gap in a ferrite or iron core, the leakage flux can be a problem to the wire turns located close by because, the flux density local to the air gap can cause a significant heating of the copper due to localized eddy current induction. This is because the flux is not "contained" within the main body of the core however, it doesn't normally cause an issue unless the power is significantly high.