... so as to force the OP to show effort.

And if you'd kept that to yourself, we might have found out if the OP had tried it.

With following the error messages and just a little effort, what I posted can become:

#! perl -slw
use strict;

for( qw[
    ab123
    'ab123s
    'ab123's
] ) {
    if(
        m[
            ^'? [a-z]               ## start with letter or an apostro
+phy followed by one
            [a-z0-9'-_]+            ## Alphanumeric + '-_
            (?: [a-z0-9] | s') $    ## ends with alphanumeric or s'
        ]x
        and not
        m[''|--]                    ## No doubled ''s or --s
    ){
        print "$_: Ok!";
    } else {
        print "$_: Bad!";
    }
}
__END__
C:\test>junk
ab123: Ok!
'ab123s: Ok!
'ab123's: Ok!
[download]

Which gives a starting point but not the whole thing.

If you're going to bother saying something, best make it something useful.