I want to take medicine to delay my period in Ramadan.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Delaying the menses period is permissible but leaving it to its natural process is better for many reasons:
a) This is a thing, which Allah has ordained for the daughter of Eve. The Muslim women follow the orders of Allah by abstaining from prayers, fasting, making Tawaf around al-Ka'ba in this period just as they worship Allah by performing prayers, fasting, etc. when they are clean. Therefore, when a menstruating woman abandons performing prayers, fasting, implementing Allah's Orders she is actually worshipping Allah and gets reward on doing so just as she gets reward on fulfilling her religious duties when she is pure. Therefore, trying to delay the period is like changing the creation of Allah.
b) Probably the pills for delaying menses may not prevent other discharges that are similar to the menses. In this case, the woman gets confused on whether it is menses or another kind of bleeding and then she cannot decide whether to perform prayers, fasting, etc. or not?
Also sometimes even after leaving the use of pills she faces disturbance in her period.
c) Many doctors do not advise women to use these pills since they may have some side effects.
Finally, we advise this sister to avoid using such pills and accept Allah's decree and continue worshipping Allah in all situations, as He prescribed.
Allah knows best.