can a first-year student apply for a PhD course's scholarship? Are there any exceptional case for excellents students at colleges desiring for a PhD

Artena, I am not quite sure where you are now. If you are in your first year at a PhD programme, then you definitely can apply for a PhD scholarship. Although you have to check with the scholarship programme if it is for entering students only, or for continuing ones as well. If you are only at first year of a Bachelor's programme, then you have to get a degree first, then apply to the PhD programme, get admitted, and only then you can apply for a PhD scholarship.