Tom
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It depends on what authority you have, what fingerprint sample you have, and where you are searching.
For example if you were a state police officer or higher in the USA you can search I.A.F.I.S. and get a result in a week if the sample was taken correctly, scanned, and sent electronically.
If you submitted the sample in another way you would have to allow more time for processing.
You can also do a search as a civil entity, but the FBI charges for the service and it is significantly slower.
I.A.F.I.S. is probably the fastest, but by no means the only database in the world. Interpol and many other individual countries have their own databases with varying response times.