There is one baptism from 1815 to 1825 that might be his:

First name(s)           Thomas
Last name               Pantan   [sic]
Baptism year            1806
Baptism date            25 May 1806
Place                   Y Betws
County                  Carmarthenshire
Country                 Wales
Father's first name(s)  Thomas
Mother's first name(s)  Jannet
Record set              Carmarthenshire Baptisms

But it needs some corroboration to be certain.
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In 1841 this family might well be them at Ynysdder, Mynyddyslwyn, Newport, Monmouthshire, Wales; he was a quarryman, on the enumerator’s sheet:

First name(s) Last name Sex Age Birth year Birth place
Thomas   Punton  Male    34  1807  -
Ann      Punton  Female  35  1806  Monmouthshire, Wales
Mary     Punton  Female  10  1831  Monmouthshire, Wales
Thomas   Punton  Male     8  1833  Monmouthshire, Wales
Hannah   Punton  Female   6  1835  Monmouthshire, Wales
William  Punton  Male     3  1838  Monmouthshire, Wales
Ann      Punton  Female   0  1841  Monmouthshire, Wales

Ref:
Archive reference  HO107
Piece number       751
Book number        8
Folio number       46
Page number        4
Combined:          HO107, piece 751, book, 8, folio 46, p. 4
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Thomas was not found in any susequent census.

Deaths for Thomas P*nt*ns found after 1841 in 1842, 1859, 1862, 1863, 1865, 1869 and 1875.  I have no idea which might be his, if any.
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Transcript of the parish register:

First name(s)           Thomas
Last name               Puntan  (Corrected from the transcription error of ‘Pentan’)
Event year              1837
Marriage year           1837
Marriage date           03 Jun 1837
Marriage place          Abergwili
Residence               Abergwili
Spouse's first name(s)  Anne
Spouse's last name      Thomas
Spouse's birth year     -
Spouse's residence      Abergwili
County                  Carmarthenshire
Country                 Wales
Event                   Marriage
Page                    30
Record set              Carmarthenshire Marriages And Banns
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