A man is obligated to provide sustenance to his sons and daughters until they are 6 years of age, even if they own property that came to them through their mother's father's house. From then and on, we provide for them as a decree of the sages until they are adults. If he does not want to, we denounce him and shame him and antagonize him [until he does]. If he [still] does not want to, we denounce him in public and say, "So-and-so is cruel and does not want to provide for his children! He is worse than a non-kosher bird that [at least] provides for its chicks!" But we do not force him to provide them sustenance. When does this ruling apply? When there is no economic estimation. But if the estimate shows that there is enough money for them to get charity, we remove it from him by force, for charity purposes, and we feed them until they become adults. Rama: This is specifically for feeding daughters [as well], but we do not force him [with regards to how much he gives] to marry off his daughters. Even though it is a mitzva to give his daughters off to those who are appropriate for them, nevertheless we do not force it, except what he prefers to give, as long as he marries them off (Hagahot Mordechai in Kiddushin, and so writes TA"V Netiv 22).
If one travels out of the country [by boat] and leaves his children behind, they [the court] sell his property for income until the children are six. From the age of six and on, they do not feed them from his property. Rem"a: Some say that is specifically when they had not started to feed them after they turned six, but if they had [already] started to feed them, they can feed them off of the [proceeds from selling] his property, for he surely would be fine with that (Mordechai Perek Neara in the name of R"Y). Some say if he had been evaluated [according to what he could give], they feed them in any case [whether they started at six or not] through it being charity (so is inferred from the Tur).
One who went insane, they provide for his sons and daughters from [selling] his property, even if they are more than six years of age, until they become adults.
A [man] who has premarital sex with a single woman and impregnates her, if he admits the child is his, he is obligated to provide food for it.