2 Answers

Sense 1 paternity 
Meaning:
The state of being a father
Classified under:
Nouns denoting stable states of affairs
Context example:
tests were conducted to determine paternity
Hypernyms ("paternity" is a kind of...):
state (the way something is with respect to its main attributes)

Sense 2 paternity 
Meaning:
The kinship relation between an offspring and the father
Classified under:
Nouns denoting relations between people or things or ideas
Synonyms:
fatherhood; paternity
Hypernyms ("paternity" is a kind of...):
family relationship; kinship; relationship ((anthropology) relatedness or connection by blood or marriage or adoption)

Sense 3 paternity 
Meaning:
The act of initiating a new idea or theory or writing
Classified under:
Nouns denoting acts or actions
Synonyms:
authorship; paternity
Context example:
the authorship of the theory is disputed
Hypernyms ("paternity" is a kind of...):
creation; foundation; founding; initiation; innovation; instauration; institution; introduction; origination (the act of starting something for the first time; introducing something new)

Paternity is the state of being a father; fatherhood. Descent on a father's side. Maternity would be the mother's side.  

These words are where we get the terms Pa and Ma from.