Is it true that people should give charity equal to the weight in silver of the shaved hair of new born. As my mother is suggesting me to do this for my new born baby?
All Praise to Allah Subhanahu wa Taala and blessings of Him be on Prophet Muhammad peace be upon him His family and companions.
Yes your mother is suggesting you a Sunnah.
"The Messenger of Allah (ﷺ) had the 'Aqiqah for Al-Hasan with one sheep, and said: 'O Fatimah! (peace be upon her) Shave his head and give the weight of his hair in silver as charity.'" He said: "So I weighed it, and it was the weight of a Dirham or a bit of a Dirham."(Tirmidhi)
"Fatima,(peace be upon her) the daughter of the Messenger of Allah, may Allah bless him and grant him peace, weighed the hair of Hasan, Husayn, Zaynab and Umm Kulthum, and gave away in sadaqa an equivalent weight of silver."(Muwatta)
Allah Swt and His Messenger knows best.