If the reality is as you have mentioned, i.e. the child suckled only once when he was three years old, it will be permissible for such a child to marry one of his paternal uncle's daughters regardless of whether their mother suckled him or not. This is because
the breastfeeding that prohibits marriage is that consisting of five or more times of suckling within the first two years of a child's life. Allah (Exalted be He) said:
The mothers shall give suck to their children for two whole years, (that is) for those (parents) who desire to complete the term of suckling
It is also authentically reported on the authority of
`Aishah (may Allah be pleased with her) that she said: "It was (Part No. 21; Page No. 41) among the revelation of the Qur'an that ten known times of breastfeeding make the marriage prohibited, but this was later abrogated and reduced to five. The Messenger of Allah (peace be upon him) died and the ruling remained effective."May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.