a=0;
while [ $a -eq 0 ]     # Needs SPACE there
do
    echo "ENTER path"
    read path
    if [ -e $path ]; then    # You forgot a ';' here
        echo "path found"
        cd $path
        DateTimeStamp=$(date '+%d_%m_%y_%H_%M')
        echo "enter file name"
        read file
        if  [ -e $file ]; then    # here too ! and needs SPACE
            echo "file exists"
            cp ${path}/${file} ${path}/${file}_bkp_${DateTimeStamp}
            echo "file backup created using file name   
            ${path}/${file}_bkp_${DateTimeStamp}"
            chmod 755 ${path}/${file}_bkp_${DateTimeStamp} 
        else
            echo "file does not exist"
            a=1    # no need of ';' here
        fi
    else
        echo "path does not exist"
        a=1    # no need of ';' here
    fi
done