The last day of my monthly period is the ninth day but I'm not sure about the exact hour of the morning so I used to take a bath after I wake up this Ramadhaan I put the alarm before al-Fajr but I didn't wake up I didn't see anything in the morning is my fasting right?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Your fasting of this day is of two situations:

One, if you intended during the night to fast the following day, and knew by habit that the blood stops before Fajr of that day, some jurists are of the view that your fast is correct. However, if you make up for it, that is safer and better in order to avoid the opinion of those scholars who differed saying that it is obligatory to make up this day due to doubt when you became pure i.e. before or after Fajr.

Two, if you did not intend during the night to fast, then your fasting is definitely incorrect, because one of the conditions of the validity of an obligatory fasting is that one makes the intention the night before. On this the scholars agree.

Finally, we draw your attention to two matters:

Firstly, if the reason that prohibits fasting is removed before the day ends, then it is more appropriate to fast the remaining part of that day to avoid the conflicting opinions of the scholars about the obligation to fast the remainder of that day.

Secondly, becoming pure after menses is known by two signs: either by noticing that there is no trace of blood, or by noticing a white liquid which comes out of the womb at the end of menses.

Allaah knows best.