There is no high quality evidence to suggest that the overall attempted suicide rate of transgender youth is 41%.
The frequently repeated claim that 41% of 6,450 transgender respondents said they had attempted suicide at some point in their lives  is taken from the National Transgender Discrimination Survey .
However, a 2021 paper  notes that the participants were recruited through transgender advocacy organizations and subjects were asked to “pledge” to promote the survey among friends and family. This recruiting method yielded a large but highly skewed sample. By targeting transgender advocacy groups, the survey underrepresented the experiences of transgender individuals who are not politically engaged. Also, a very high number of the survey participants (nearly 40%) had not transitioned medically or socially at the time of the survey, and a significant number reported no intention to transition in the future.
A 2016 article  analyzes the power of this 41% statistic, investigating how it has affected conversations about the injustices transgender people face and the importance of family and societal acceptance.
 Turban, J. L., Beckwith, N., Reisner, S. L., & Keuroghlian, A. S. (2020). Association between recalled exposure to gender identity conversion efforts and psychological distress and suicide attempts among transgender adults. JAMA Psychiatry 77 (1): 68-76. [Link]
 Grant, J. M., Mottet, L. A., Tanis, J., Harrison, J., Herman, J. L., & Keisling, M. (2011). Injustice at every turn: A report of the national transgender discrimination survey. National Gay and Lesbian Task Force; National Center for Transgender Equality. [Link]
 D’Angelo, R., Syrulnik, E., Ayad, S., Marchiano, L., Kenny, D.T. & Clarke, P. (2021). One Size Does Not Fit All: In Support of Psychotherapy for Gender Dysphoria. Arch Sex Behav 50: 7-16. [Link]
 Tanis, J. (2016). The power of 41%: A glimpse into the life of a statistic. Am J Orthopsychiatry, 86 (4): 373-7. [Link]