In his 30-page petition, filed yesterday in the Bandra court, Paes alleges that Rhea's "escapades, indiscreet and irresponsible behaviour, lack of personal maternal supervision, volatile temper and self-indulgence created insecurity in the child and was detrimental to a healthy upbringing".
As per the law, custody of a child born to a couple in a live-in relationship generally goes to the mother, unless the father establishes that child's upbringing would suffer in the mother's care.
Meanwhile, Paes has also approached the city police alleging that his daughter was in danger and she may be forcibly taken out of the country by Rhea.
Paes submitted an application to Mumbai Police Commissioner Rakesh Maria, who forwarded it to Additional Police Commissioner Milind Bharambe to look into the matter, police sources said.
His petition said his relationship with Rhea started in 2003 when they met on a flight, however, they never married "because Rhea did not believe in the institution of marriage due to a failed relationship experienced by her earlier".
It alleges that Rhea told him wrongly in 2005 that she had divorced actor Sanjay Dutt, while the couple's divorce by mutual consent came only in 2008 and Paes learnt about it only in 2013.