Ttest and heteroscedasticity problem in no intercept model

I was running a t test over two regression betas with the assumption of equal variance. I know that if the condition of homoscedasticity do not hold then there are chances to have type 2 error but what if in my regression I do not have the intercept? (The models without errors do not require the error mean to be zero). I am very confused, I may have mixing two different concepts so, please tell me the associated readings to get it more clear.