Hindi has many verbs consist of postpositional phrase, that is, some verbs are followed by postpositions. some of them are the following.....
1. To meet = se milnaa
2. To wait for someone/something - kisee ka intazaar karnaa
3. To listen to someone = kisee ki sunanaa/kisee ki baat sunanaa
4. To ask = se puchhnaa
5. To marry = se shaadi karnaa
6. To talk to = se baat karnaa
When object pronoun "mujhe" (me), is followed by postposition ka/ki/ke/ke liye ,mujhe becomes meraa=(mujhe+ka), meri=(mujhe+ki),mere=(mujhe+ke), mere liye (mujhe+ke liye) for example - He is waiting for me - vah/vo meraa(mujhe+ka=meraa) intazaar kar rahaa hai. (to wait for someone/something -ka intazaar karnaa)
Now let me answer your question.
To listen to someone (kisee ki sunanaa/kisee ki baat sunanaa)
My heart does not listen to me nowdays - meraa dil aaj kal meri (mujhe+ki=meri) nahi suntaa hai (in this example mujhe (me) is followed by postposition "ki" that is reason mujhe is changed into meri
More examples - He does not listen to me - vah/vo meri nahi suntaa hai/ vah meri baat nahi suntaa hai
She only listens to her mother - vah keval apni maa ki suntee hai/ vah/vo keval apni maa ki baat suntee hai
Boss will not listen to me. Boss meri nahi sunegaa/ boss meri baat nahi sunegaa