You can just put mylist inside [] and pandas will select it for you.

mydata_new = mydata[mylist]

Not sure whether your yyy is a typo.

The reason that you are wrong is that you are assigning mydata_new to a new series every time in the loop.

for item in mylist:
    mydata_new = mydata[item]  # <-  

Thus, it will create a series rather than the whole df you want.

If some names in the list is not in your data frame, you can always check it with,

len(set(mylist) - set(mydata.columns)) > 0

and print it out

print(set(mylist) - set(mydata.columns))

Then see if there are typos or other unintended behaviors.