Is there any Q&A site under the Stack Exchange network where we can discuss about supernatural incidents? If not, then whom should I petition to create it?
There currently is no Stack Exchange site for that topic.
There are proposals for such sites on Area 51, e.g.:
There have been proposals before, that did not make it through the process (for various reasons).
Basically Area 51 is the place to propose new Stack Exchange sites if there isn't one yet.
[…] where we can discuss about […]
Stack Exchange sites in general are not for discussion of anything. The notable exception are the meta sites where discussion about the site itself does happen.
As others have mentioned Area 51 is the place for proposing new Question and Answer sites for the network. It is possible to discussion the viability of such a site there, and I believe you have been pointed to a couple of related proposals. However it is important to note that these are proposals for QnA sites, not discussion forums. In order to prove viability, one of the requirements is that they define a scope for questions which will be factually answerable in a QnA format.
You can recommend ideas for the Stack Exchange Network on Area 51. This site facilitates discussion about the idea with other members and if enough people agree to use the site, it can be launched in beta mode etc. For more information on this, see the Area 51 FAQ.
Edit: As Martijn notes in his answer, there are two suggestions for such sites on there already. Refer to his answer for the links.