No Scripture. Just the Traditions of the first generation of the Church. Which occurred before most NT Scripture was even written.
The book of Acts covers about 30 years of church history from the Day of Pentecost on. That sounds like the first generation of church history to me. And Luke compiled a very concise, methodical account of that first 30 years, and never mentioned the Peter stuff, although one could presume that since Luke traveled with Paul, he would have had opportunity to actually meet Peter.
It appears that Luke joined up with Paul and started traveling with him in Acts 16 for a brief time, and then in Acts 20. He traveled with him to Jerusalem and met James, at least, and the other elders. While Peter is not mentioned specifically by name, it is not unlikely that Luke either met him or heard of him, but there is no mention of either being done. That would be quite an oversight if Peter had indeed been given such a place of preeminence.
If those traditions of men occurred BEFORE most of the NT Scripture were written, then why weren’t they incorporated into the Scripture that was written AFTER those traditions were allegedly established?