Hi all. how I can apply the image sequence to the sprite based on the birth time and also is it possible to apply 2 types of image sequence? Any help would be greatly appreciated. Thanks in advance.

the way to do this is to create custom string attribute for every point of your particle system, that will override path to texture in sprite shader. Using expressions you can control, from what directory and what exactly texture will be loaded for every sprite at current frame
See the attached file, it will become clear

Thank you for uploading the scene file. Now I got what I was looking for. The expression using fit,round with $LIFE make so sense. Thanks again.