I am using version 8.7 of TYPO3 and intended to use a link that leads directly to the backend to edit a record (page). I tried anything like typo3/backend.php?edit=57 but got a error:
file not found
typo3/backend.php?edit=57 was the way to do it up until TYPO3 6.2, but the backend URL changed to typo3/index.php in TYPO3 7.6. It still works kind of, however you need a security token which is generated by the core. The URL now is typo3/index.php?route=%2Fmain&edit=57&token=.... There isn't really an easy way to generate URL with a valid token like that from outside TYPO3 though.
If you want to create a link inside a custom module to edit a record you can use \TYPO3\CMS\Backend\Utility\BackendUtility::editOnClick() or if you're using a Fluid template, the \TYPO3\CMS\Backend\ViewHelpers\Link\EditRecordViewHelper ViewHelper. More on that you can find here: https://docs.typo3.org/typo3cms/CoreApiReference/8.7/ApiOverview/Examples/EditLinks/