We have many publication in Tridion 8.5 where certain set of group is parent for specific publication. So if a try to publish any items from parent publication in the Publishing pop-up i can't live Target live where to publish stag or live. So anyone please suggest where configuration needs to changed or looked in to for the same :)
If I understand your question correctly, then the problem is that the Staging and Live Target Types do not show up in the Publishing Dialogue when you try to publish an item (e.g. a Page or Dynamic Component Presentation).
You would like to use the Also Publish/Unpublish in Child Publications option (within the Advanced tab) from the Parent Publication, but are unable to use this because the Target Types are not showing in the Choose One or More Target Types to Publish to pane.
Assuming that I've understood the question correctly, then the most likely cause is that publishing is not configured for the Parent Publication or you don't have rights to publish from that Publication.
You'll need to configure publishing within Topology Manager (or the Legacy Publishing GUI) for the Parent Publication (and possibly in the Deployer configuration).
You may also want to look in the Security tab of the Publication Properties to confirm that your User/Group has the Publish to Content Distributor option checked.