Make sure the backlinks are on pages that are not noindexed (they neither have a meta noindex tag nor a noindex http header), as well as the pages’ URLs not matching any rule on their website’s robots.txt file.
Additionally, make sure that the page on your own website the backlink points to doesn’t match a rule on your site’s own robots.txt
If all that checks out, you can go to Ahrefs.com and set up a free account and see if Ahrefs can detect the backlink.
Something else to check out is DaniWeb’s SEO backlink checker at https://www.daniweb.com/tools/backlinks
To use the tool, enter your own domain name as well as a list of URLs that you expect your backlinks to appear on. It will check each of the URLs and make sure that there are no meta noindex tags, http noindex, robots.txt rules, etc., and if there’s any technical reason why the backlink shouldn’t be found, so you don’t have to do all of that manually.