Script for incremental saving

... Now everything is sorted like what I needed. Totally tried and tasted it. Many Thanks!!

By @Azmaeen Adil Sami

Glad to help. So the only outstanding issue is changing the file naming counter to name the first file as 601 (rather than 001), then increment it by 1 for each new file saved thereafter? 

@Azmaeen Adil Sami 

You can try the following script. Don't use Automate > Batch anymore, this is a batch script. You will be prompted for an input folder and output folder.

Please note: you need to change the case-sensitive name of the action and action set in the script to your specific names.

Remove any PNG saving steps from your action, the script now does that. If required, add a save step for the updated PSD, as the script closes all PSD files without saving any changes.

/*

Batch Sequential Incremental Filename to PNG.jsx

https://community.adobe.com/t5/photoshop-ecosystem-discussions/script-for-incremental-saving/td-p/13235725
v1.1 1st October 2022 - Stephen Marsh

Based on:
https://community.adobe.com/t5/photoshop-ecosystem-discussions/repeat-action-and-save-file/td-p/8532556
https://community.adobe.com/t5/photoshop/saving-sequential-file-names-of-the-same-file-to-multiple-files/td-p/12023959 

*/

#target photoshop

// Change the action and action set names to suit (Case Sensitive)
var actionName = "Molten Lead"; // Action to run
var actionSet = "Default Actions"; // Action set to run

// Disable dialog display
var restoreDialogMode = app.displayDialogs;
app.displayDialogs = DialogModes.NO;

(function () {
    
    // Select the input directory
    var inputFolder = Folder.selectDialog("Please select the input folder:");
    if (inputFolder === null) {
        // alert('Script cancelled!');
        return;
    }

    // Get the Photoshop files
    var fileList = inputFolder.getFiles(/\.(psd|psb)$/i);

    // Force alpha-numeric list sort
    fileList.sort().reverse();

    // Validate that the file list is not empty
    var inputCount = fileList.length;
    var folderSelection = (inputCount === 0);
    if (folderSelection === true) {
        inputFolder = Folder.selectDialog("No files found, please reselect the input folder:");
        return;
    }

    // Select the output folder
    var outputFolder = Folder.selectDialog("Please select the output folder:");
    if (outputFolder === null) {
        // alert('Script cancelled!');
        return;
    }

    // Start the file count saving counter at zero
    var counter = 0;

    // Loop over the input files
    while (fileList.length) {
        for (var a = 0; a < 1; a++) {
            try {
                app.open(fileList.pop());
            } catch (e) {}
        }
        app.doAction(actionName, actionSet);
        incrementalSave();
        activeDocument.close(SaveOptions.DONOTSAVECHANGES);
        // Increment the file count saving counter for each loop
        counter++;
    }

    function incrementalSave() {
        try {
            var name = activeDocument.name;
            var n = name.lastIndexOf(".");
            if (n > 0) name = name.substr(0, n);

            // Starting number (+1), 99 would start at 100
            var indexNo = 0;

            do {
                // Zero padding file name, last number ending in 4 = 0001 or ending in 3 = 099 etc.
                var seqNo = zeroPad(indexNo + 1, 4);
                
                // Save path and filename
                var file = new File(outputFolder + "/" + seqNo + ".png");
                ++indexNo;
            }

            while (file.exists)
            var saveOptions = new PNGSaveOptions();
            // Range from 0 Largest file size to 9 smallest file size
            saveOptions.compression = 0;
            saveOptions.interlaced = false;
            app.activeDocument.saveAs(file, saveOptions, true, Extension.LOWERCASE);
            function zeroPad(n, s) {
                n = n.toString();
                while (n.length < s) n = '0' + n;
                return n;
            }

        } catch (e) {
            alert(e);
        }
    }

    // End of script notification
    app.beep();
    alert('Script completed!' + '\r' + counter + ' files saved to:' + '\r' + outputFolder.fsName);

    // Restore the dialogs
    app.displayDialogs = restoreDialogMode;

}());

Edit: Original code updated to v1.1

https://prepression.blogspot.com/2017/11/downloading-and-installing-adobe-scripts.html