You can do a quick search of census data at www.ddd.dda.dk
At Arkivalieronline (AO) you will find more complete records.
I found this boy. The parents aren’t here, but grandfather was a fisherman…
Frederiksborg, Lynge-Kronborg, Asminderød, Sletten, et hus, 46, FT-1834, B5811
Jacob Jensen 57 Gift fisker
Maren Jacobsdatter 58 Gift hans kone
Grete Jacobsdatter 27 Ugift deres børn
Rasmus Jacobsen 24 Ugift deres børn
Johanne Jacobsdatter 18 Ugift deres børn
Jens Nielsen 14 Ugift borne born
Jens Hansen 5 Ugift børnebørn
The next step would be to go to the churchrecords for his parents.
Probably it's better to trace him step by step back in time to find his family in Denmark. Do you have more info? (siblings, children, year of immigration, a death record with precise birth year, etc.) A cluster of names can sometimes help in identifying a person - the more the merrier.