According to Israeli law, parents do not have any ownership rights in the monetary assets that their children receive even when they are under the age of 18 and are under their parents’ auspices. We will now look at what halacha has to say about the matter from a fundamental perspective, without factoring in the effect of the concepts of the law of the land and local practice. We will have to keep in mind that there are distinctions in halacha in this regard depending on the child’s source of receiving the money.
We will start with lost objects that a child found. The mishna (Bava Metzia 12a) says: "That which a minor son or daughter finds goes to the father; that which an adult son or daughter finds is theirs." The gemara cites a machloket among Amora’im on how to draw the line between minors and adults in this regard. According to Shmuel, a minor in this regard is one below bar mitzva and an adult is past bar mitzva. Rav Yochanan says that a minor is one who is dependent on his "father’s table" for basic support, whereas an adult is one who is financially independent. The halacha is like Rav Yochanan (Shulchan Aruch, Choshen Mishpat 270:2). Therefore, if the average teenager, who is supported by his father, finds something, the object goes to his father. The reason is to avoid antagonism of the father toward a son who takes his father’s support, yet does not contribute that which he finds. In theory, the same is true of a 40 year old who is supported by his father. The Maharitatz (233) says that the same is true of one who does not live in his parents’ house but relies on them for basic support. The Smak and the Kolbo say, though, that a married son, even if he is is supported by his father, does not have to give the father that which he finds. They posit that, by definition, a married child cannot be considered "reliant" on his father.
Tosafot (Ketubot 47a) says that there is a distinction in this regard between a son and a daughter (of more theoretical than practical consequences in our society). A daughter who is under the age of twelve and a half gives her father that which she finds even if he does not support her. The reason is that since he is capable of marrying her off to someone whom she may not be happy with, the concept of avoiding antagonism applies even when he is not supporting her. [Ed. note- one might add that specifically regarding one who, either out of desperate financial straits or out of animosity, is not supporting such a young child could be suspected of preferring other factors to the his daughter’s welfare.]