With zsh:

autoload age # best in ~/.zshrc if you use that often
ls -ldS -- *(De:age 2018-06-01 2018-06-30:OL[1,20])

With zsh:

autoload age # best in ~/.zshrc if you use that often
ls -ldS -- *(De:age 2018-06-01 2018-06-30:OL[1,20])

• -S: sort by size. With GNU ls (as found on RedHat 5.3), you can use -U for not sorting as zsh has sorted the list already with OL.
• (...): glob qualifier
• D: don't ignore dot files.
• e:code: evaluate the code to decide whether to select the file
• age date1 date2: returns true for files with mtime in that range (without time part, it defaults to 00:00:00)
• OL: reverse sort by length (size)
• [1,20]: only select the first 20 ones.