Find all files with a filename beginning with a specified string?

Use find with a wildcard:

find . -name 'mystring*'

If you want to restrict your search only to files you should consider to use -type f in your search

try to use also -iname for case-insensitive search

Example:

find /path -iname 'yourstring*' -type f

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You could also perform some operations on results without pipe sign or xargs

Example:

Search for files and show their size in MB

find /path -iname 'yourstring*' -type f -exec du -sm {} \;

ls | grep "^abc"  

will give you all files beginning (which is what the OP specifically required) with the substringabc.
It operates only on the current directory whereas find operates recursively into sub folders.

To use find for only files starting with your string try

find . -name 'abc'*