Self-funding alone need not be visible in your applications and is unlikely to hurt in any case. That said, getting outside funding is likely to help and you should pursue it if you can.

First, it's not clear how any potential employer would know that you were self funded. Although it's normal to list fellowships or funding that you have received, it's just not normal (in my experience) to list the amount of money you received from a particular fellowship/grant unless it was a very public award.

That said, a list of grants, fellowships, and outside funding will help build a stronger CV. One thing many search committees are looking is a demonstrated ability to bring in grants and funding. Although that can be hard to discern in a graduate student/post-doc, the ability to apply for and get student fellowships can bring a little comfort. Being able to point out in your coverletter that you've thought about grants will inspire a little confidence in your application.

But the standard answer to questions of the form "does x matter for the job market" still applies. The quality of your work, your publications, your letters, and many other things will weight much more heavily than the fact that you don't have fellowships that others do.

Self-funding alone need not be visible in your applications and is unlikely to hurt in any case. That said, getting outside funding is likely to help and you should pursue it if you can.

First, it's not clear how any potential employer would know that you were self funded. Although it's normal to list fellowships or funding that you have received, it's just not normal (in my experience) to list the amount of money you received from a particular fellowship/grant unless it was a very public award.

That said, a list of grants, fellowships, and outside funding will help build a stronger CV. One thing many search committees are looking is a demonstrated ability to bring in grants and funding. Although that can be hard to discern in a graduate student/post-doc, the ability to apply for and get student fellowships can bring a little comfort. Being able to point out in your coverletter that you've thought about grants will inspire a little confidence in your application.

But the standard answer to questions of the form "does x matter for the job market" still applies. The quality of your work, your publications, your letters, and many other things will weigh much more heavily than the fact that you don't have fellowships that others do.