Welcome and thanks for posting your query to HealthcareMagic.
As per your query you have noticed sunken purple patch on buttock. You have not mentioned in your query the exact time period since the patch is present.
As you mentioned you noticed after the child birth so it can be possible form the mid atrophy
of the skin by injections at the buttock. During child birth there are multiple kind of injections are being given. So any of the injection in the fat can cause mild atrophy.
Now the exact diagnosis can only be given by doing biopsy of the skin. So if you are really worried then can go for skin biopsy
I hope these information's will help you. If you have further queries I will be happy to help.
Dr Sanjay Kumar Kanodia