Prince says to set aside a card costing up to $4. Does that apply to cards like Mercenary or Fugitive (costing $0* and $4* respectively) because they are not in the supply? I suspect yes (and played as such) because it doesn't say 'in the supply', just 'from your hand'.
Yes, the asterisk is just a reminder that there's something weird going on there (such as the inability to actually buy the card, or the cost-changing of Peddler). A card with a cost of $4* actually has a cost of $4 and so can be set aside with Prince. Ditto for e.g. $4+ on Herald.