I was soldering a magnet wire with a normal copper wire, and while doing that, i burned a small part of the magnet wire, so will this affect the conductance of the wire??
Most likely you burned the insulation, not the copper part of the wire. Be aware that burned insulation no longer insulates, but also creates a layer that makes soldering difficult.
It's not clear what part of the wire you burned, and whether this was accidental or not. If you deliberately burned the end to remove the insulation, then finish the job by lightly scraping it off. Once you get bare copper color, it will solder fine. If you burned some other part of the wire accidentally, like part of a coil that is already wound, you may have problems. Look carefully to see if adjacent windings are now touching. You might be able to fix this by brushing off or very carefully scraping off the burnt insulation, then fixing the wire in place with epoxy after making sure nothing is touching.
If it is in a coil then the answer is possibly. If the cross sectional area has been reduced then 'yes'. If you just burned the insulation on the outside then 'no'. See if you can zoom in on it with a camera, microscope or magnifying glass. Will it hurt? That depends on your application. If you can, clip off the burnt end and try again. You may want to use a lower temperature on your iron. Also make sure the burned end that may be devoid of insulation is not 'connecting' to any other conductors.
I usually burn the enamel off the magnet wire by turning up the soldering iron to about 800F and (dipping the tip of the enamel wire in fosin flux) and then onto a hot solder glob. Conductance is proportional to cross sectional area, temperature, and the conductivity of the material so no you aren't going to affect the conductance by removing the enamel coating. But like others have said it depends on your application.