Can he give to one of his children and not the others if he is poor?

Some of the scholars said that it is permissible to show preference to some children in giving, if there is a shar’i justification for that, such as if one of them is disabled or has a large family or is preoccupied with seeking knowledge, or if one of them is an evildoer or innovator, he may withhold some money from him. 

Ibn Qudaamah (may Allaah have mercy on him) said: If he singles out one of them because he is in need, or he is chronically ill, or he is blind, or he has a large family, or because he is preoccupied with seeking knowledge, or other reasons, or he refrains from giving to one of them because he is an evildoer or an innovator, or because he will use what he takes to disobey Allaah, or spend it on such things, then there is a report from Ahmad which indicates that that is permissible, because he said with regard to singling out one of them for a waqf: there is nothing wrong with that if it is for a need, but I dislike it if it is by way of showing preference. A gift is like a waqf. The apparent meaning of his words may be understood as meaning that it is not allowed to show favour to or single out one of them in any case. End quote from al-Mughni (5/388) 

It says in Fataawa al-Lajnah al-Daa’imah (16/193): What is prescribed with regard to giving gifts to one's children is to give them gifts equally; it is not permissible to favour one over another unless there is a shar’i justification, such as if one of them is disabled or  has a large family or is busy seeking knowledge, or he may refrain from giving to one of his children because of his evil or innovation, or because he will disobey Allaah with what he takes. End quote. 

See also al-Fataawa al-Kubra by Shaykh al-Islam Ibn Taymiyah (5/435) 

And Allaah knows best.