>'“Which Purana talks about the incident of Lord Shiva saving The Sage Markandeya?” None of them, it’s just folklore.' 

writes somebody. 

This is false - since sthalapuranas are also puranas.

It is the sthlapuranam of an illustrious temple -Tirukkadaiyur Abirami temple - and many devotees recite the Abirami Andadi prayer dedicated to goddess Abirami.  Because of the Markandeya story, couples come here to celebrate the husband's sixtieth birthday - believing that they would get long life also.

http://gcmouli.com/blog/tag/thirukadaiyur/

>When the Devas and Asuras churned the ocean and got the nectar, they forgot to worship Lord Ganesha. Lord Ganesha was upset about this, and stole the pot (ghata) of nectar and hid it here in Thirukadaiyur. He created a Shiva Lingam to worship his parents and did abhishekam with the nectar. It is because of this (and the Markandeyar story) that, folks believe that if they come here, they are blessed with long years of life.

>Before Markandeyar was born, his father Sage Mrukandu was given a choice – a wise boy who will not cross 16 years, or a mediocre boy who will live longer. His parents chose the first option. On the 16th year, when Lord Yama came for Markandeyar, Markandeyar hugged the Shiva Lingam. Lord Yama unleashed the death leash and it surrounded the Shiva Lingam as well. Lord Shiva became very cross and kicked Lord Yama and gave Markandeyar immortality and Moksha.

I believe this story is in the thevaram - if I get hold of it, I'll post that also.

the legendary Ravi Verma has immortalized the story with one of his portraits. 

https://www.google.com/search?q=ravi+verma+markandeya&client=firefox-b-1-d&tbm=isch&source=iu&ictx=1&fir=QevbleokfRoMQM%253A%252CbjjjgdwIFLZEBM%252C_&vet=1&usg=AI4_-kT63o-DMay9jG3a82xsHaH1QnipHQ&sa=X&ved=2ahUKEwi1wNmM3-vnAhVQneAKHQ7yC7AQ9QEwBHoECAkQBQ#imgrc=QevbleokfRoMQM: