Any adjective can go after quelque chose de:
Quelque chose de petit/de vrai/d'authentique/de beau/de grand/de spécial.
Not all adjectives can go before what they refer to and often, the meaning is different depending on this location. Most of the adjectives appearing in the question might be used before quelque chose though.
Un petit quelque chose is a common set expression.
Un vrai quelque chose, un authentique quelque chose, un beau quelque chose, un grand quelque chose are less common but correct.
The only one in the list that doesn't work is spécial, but that's because spécial is always after the word it qualifies.
See Quand peut-on mettre un adjectif avant ou après un nom ? — When do adjectives go before or after a noun? and a francaisfacile.com page that talks about adjectives position.
About the difference between quelque chose de petit and un petit quelque chose:
— Je lui ai offert un petit quelque chose pour Noël.
I gave him/her a little thingy for Christmas. Here what matters is the intention: to offer a gift.
— Je lui ai offert quelque chose de petit pour Noël.
I gave him/her something small for Christmas. Here what matters is the physical size of the present. Maybe the recipient had to travel afterward and/or has not enough room to store presents, thus something big would have been cumbersome.