Peer-reviewed, published research does not support any kind of link between vaccines and autism: not a link by correlation, not a link by cause.
There was a paper a long time ago where the guy who wrote it committed fraud to get published. This paper, which was founded on lies, did claim a link, and did so in a highly influential medical journal - so a lot of people paid attention to what the article said, even though its claims were never true. Retraction is a very definitive way to signal to scientists not to pay attention to a particular paper.
Problem is, the retraction took more than 10 years, and in those years the internet was becoming social and available to everyone. So there was kind of a perfect storm of misinformation propagation about this particular topic.
Fact remains: many many studies have re-examined the possibility of link between vaccines and autism and there just isn't one.
- Despite numerous failures in the integrity of the peer review and editorial process (Deer, 2020), the predicted high impact of this article influenced the Lancet decision to publish [0]
- There is no shortage of authors willing to publish weird stuff in scientific journals. Search for example articles about religious content in scientific papers such as these ones: [1-3]
[0] https://acamh.onlinelibrary.wiley.com/doi/10.1111/jcpp.14058
[1] https://pubmed.ncbi.nlm.nih.gov/38756930/