If you have set up a redirect from your old blogspot URLs to your new URLs, then links pointing to the old URLs will redirect to the new site. If you have not redirected from blogspot (and it no longer exists) then those links will be lost.
If your site is still hosted on blogspot and can now be reached by either URL, then links pointing to either will count as backlinks. In this case, do not start duplicating all the existing links. If possible, update them, but don’t create new ones from the same sites.
As @SamA74 has already said, search engines give very little value to links which you can place yourself, and duplicating such links may well start to look like a violation of guidelines.