How can I check for basename (only part of the name) file existence using Python?

Try glob for it:

from glob import glob
if glob('/d/prog/*data.txt'):
    # blah blah 

You can't just do it with os.path.exists -- it expects full pathname. If do not know exact filename, you should first find this file on filesystem (and when you do, it proves that file exists).

One option is to list directory (-ies), and find file manually:

>>> import os
>>> file_list = os.listdir('/etc')
>>> [fn for fn in file_list if 'deny' in fn]
['hostapd.deny', 'at.deny', 'cron.deny', 'hosts.deny']

Another and more flexible option is to use glob.glob, which allows to use wildcards such as *, ? and [...]:

>>> import glob
>>> glob.glob('/etc/*deny*')
['/etc/hostapd.deny', '/etc/at.deny', '/etc/cron.deny', '/etc/hosts.deny']

If you are on Windows:

>>> import glob
>>> glob.glob('D:\\test\\*data*')
['D:\\test\\data.1028.txt', 'D:\\test\\data2.1041.txt']