I'm reading a job description where it mentions "3 Month Paternity Relief Contract". That doesn't make sense to me. Does it mean employee can leave 3 months for paternity leave?
Paternity leave is time taken off by a new father to care for his child. The equivalent for a new mother is maternity leave. Most countries have a law which mandates that employers must give new parents time off. To cover their absence, short-term contracts are often offered.
In this case, it appears the job advertised is to cover a three-month period of paternity leave. This would be a temporary contract. This may be unsuitable if you are looking for a permanent position. However, some employers may consider hiring someone who has filled in for a person on parental leave if they do a good job and they have vacancies, it may be worth asking if this is possible.
Paternity leave is part of Parental leave.
It is an employee benefit that provides paid or unpaid time off work to care for a child or make arrangements for the child's welfare. The term "parental leave" includes maternity, paternity, and adoption leave. Often, the minimum benefits are stipulated by law.
So this contract is for 3 months only when someone who is on leave is to come back to the workplace. He/she holding his/her position and job open over the contract period.