Snapchat does not provide a built-in feature to directly see who has taken screenshots of your public story. Unlike private snaps, where Snapchat notifies you when someone takes a screenshot, the same functionality is not available for public stories. However, there are a few indirect methods you can try:

Story Views: Open your public story and swipe up on the screen to access the Story Views. This will show you a list of users who have viewed your story. While it doesn't explicitly indicate who took a screenshot, you can infer that someone may have captured your content if their username appears in the view list but they didn't engage with your story through direct messages or replies.
How To See Who Screenshotted Your Snapchat Public Story?
Snapchat Score: Another way to potentially identify if someone took a screenshot of your public story is by monitoring their Snapchat score. If you notice a sudden increase in someone's score after you posted your story, it could be an indication that they took a screenshot. However, keep in mind that Snapchat scores can also increase due to other activities, such as sending snaps, receiving snaps, or engaging with other content on the platform.

Third-Party Apps or Services: Some third-party apps or services claim to provide screenshot detection for Snapchat, but it's important to exercise caution when using them. Snapchat strictly prohibits the use of third-party apps, and using such apps can lead to your account being suspended or permanently banned. Additionally, these services may violate your privacy and compromise your account security.

It's worth noting that Snapchat emphasizes privacy and temporary content, so it's generally best to assume that anything you post on a public story can be captured by others. If you have concerns about screenshots or the privacy of your content, it's advisable to be mindful of what you share on public platforms like Snapchat and consider adjusting your privacy settings accordingly.