In after hours trading, if I wanted to buy a stock and the closing price was $3.00, the Ask price was $3.50 and the Open is $3.75. What would be the price of the stock when purchased after the closing bell?
Applicable to trading in the US:
The opening price has nothing to do with any orders placed later in the day.
The short answer is that if the size of your "limit" order is less than or equal to the available size at $3.50 then you'll be filled at $3.50 (maybe).
Unfortunately, it's not always that simple.
If the size of your limit order is larger than the ask volume at $3.50 then you'll get a partial fill unless someone else comes in to sell you the balance at $3.50
If you place a "market" order to buy and the market size at $3.50 is less than the size of your order then you'll get a partial fill at $3.50 and more shares at a higher price.
After hours trading is a different beast for illiquid stocks. Sometimes you can hit the bid or the ask and the quote will disappear with no fill. Cancel the order and the quote will reappear. Place the order again and the quote fades.
Coincidentally, this happened to me at 16:00:08 today after quick price bump 15 seconds before the closing bell. I couldn't get the order in fast enough. The only way around it is with Level II and route directly to the exchange offering the shares. I don't have Level II since this doesn't happen frequently enough to warrant the cost. This example most likely doesn't apply to your proposed trade because it's highly likely that with a 50 cent B/A spread, there would be many traders happy to fill at that price.