how do I get files that look like the target file?

Assuming that you are looking to match all .md files that "look like" - defined here as containing the sub-string readme (case insensitive) - from within the directory specified by my_dir and all sub-directories contained within, the following should work for you.

import glob
import os

my_dir = 'my_dir' # IMPORTANT Please note that the leading '/' has been removed, this is to allow for desired behaviour in os.path.join() below

files = [ i for i in glob.glob(os.path.join(my_dir, '**', '*.md'), recursive=True) if 'readme' in os.path.basename(i.lower()) ]
if files:
    # do stuff

It makes use of the builtin os module to construct the path passed to glob.glob that will search the top-level directory passed as the my_dir variable recursively and return all paths ending with a .md file.

The list of .md file paths returned by the invocation of glob.glob is filtered (by way of a list comprehension) to only include paths ending in .md files containing the sub-string readme (case insensitive).

The result is a list of all paths from within the my_dir tree that end in an .md file containing the case insensitive sub-string readme within the filename portion of the path - or an empty list if none are found.

Loop through the list of files in your directory and compare with re.search:

import re
files=['README.md','readme.md','my_readme.md','what.md']
query='readme.md'
print([file for file in files if re.search(query , file, re.IGNORECASE)])

Get a list of all file names source

from os import listdir
from os.path import isfile, join
files = [f for f in listdir(mypath) if isfile(join(mypath, f))]

Loop through each file name, and check if the lowercase version includes fname

for name in files:
    if fname in name.lower():
        print(name)

If you want to find all files, then looking at the link i provided earlier you can find the following code to find all files:

from os import walk
files = []
for (dirpath, dirnames, filenames) in walk(mypath):
    files.extend(filenames)