Ragnar and his sons mainly appeared in medieval Icelandic saga traditions, recorded about 4 centuries later than the alleged events. This is one of FAQs in this subreddit on the Vikings in general, and many answers have been given to their historicity, including mine. You can check some of them below:

• /u/Platypuskeeper writes on the historicity of Ragnar himself in: Ragnar Lothbrok, by far my favourite character in Vikings, but how much about him is true? Who were his actual sons?.
• /u/sagathain focuses on the historicity mainly of Ragnar's sons in: How can Ragnar Lodbroks children be considered real historical figures, but Ragnar himself is still considered to be mostly fictitious?
• I also wrote a bit that the legend making process around Ragnar had already occurred in the Middle Ages in: https://old.reddit.com/r/AskHistorians/comments/dqlim5/vikings_and_ragna_lothbrok_and_his_5_sons_how/