find . -iname "*a*" -executable -type f
The find command is quite powerful; if you type 'man find' this will give you a description of the many parameters.
The example above looks in the current directory '.' (and all subdirectories) for a file with an 'a' in it (-name "*a*"), which has the execute permission set (-executable), and which is of type file (-type f). The reason for restricting the type is because directories also have execute permission, for reasons I won't go into here.
At a later point if you need instead to search by files by content rather than external attributes, you would make use of a command line program called 'grep'.