NameDEMETRIUM REGANDate of BirthN/R N/R N/RAddressN/RFatherDIONISI REGANMotherELENA HULENY - Huleny a mistranscription?
It has Cornelius's baptism with parents
NameCORNELIUS REGANDate of BirthN/R N/R N/RAddressN/RFatherDEMETRIUS REGANMotherELLENA HENESEY
roots has 23 Regan - McCarthy marraiges in Cork starting 1809; marriages were usually in the bride's parish so the recotrd would not necessarily be from Bandon.
Jeremiah baptisms Cork start in 1817 on roots; this is the only one from 181:
Name:Jeremiah ReganDate of Birth:
Date of Baptism:08-May-1818Address:Not RecordedParish/District:MACROOMGender:MaleCountyCo. Cork
Father:John ReganMother:Johanna BrienOccupation:
Sponsor 1 /
Informant 1:James Regan Sponsor 2 /
Informant 2:Margaret Regan
FATHERS NAME L[JOANNIS] MOTHERS NAME L[JOANNA]
1ST SPONSORS NAME L[JACOBO] 2ND SPONSORS NAME L[MARGRETA]
roots has no earlier records than 1818 for Denis / Demetrius baptism so couldn't make a connection with John (above); you might like to try on irishgenealogy
The other place to try is the R C registers https://registers.nli.ie/ as early Bandon baptisms and marriages are available (free)