First of all, don't post screenshots of your data. Provide reproducible examples. It makes it easier for people to answer your question:
Here is an example of what you are after using the iris dataset. You can adapt it to your problem.
library(dplyr)
iris %>%
group_by(Species) %>%
arrange(Petal.Length) %>%
slice(1)
For you, group by the PatientID, then arrange by the date or exam count.
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