can i send money thru apple pay using my checking account as a source for the funds

Do you have a debit card associated with your checking account? There is no fee if the funding is from a debit card. See the following from Send, receive, and request money with Apple Pay - Apple Support

Your Apple Pay Cash balance is automatically used when you send money. If you don't have enough balance for the payment, the remainder will be funded by one of your credit or debit cards in Wallet. If you have no Apple Pay Cash balance, you can use a credit or debit card in Wallet for the entire payment amount. You can see which card is being used on the confirmation screen.

Here's how to change your payment method:

1. Tap  next to your credit or debit card on the confirmation screen.
2. Choose a new credit or debit card. If the payment is split, you can
3. see two cards on the payment sheet: your Apple Pay Cash card and the
4. other card that you choose to fund the transaction. 

• • If you choose a debit card or pay with your Apple Pay Cash balance, there’s no fee. 
  • If you choose a credit card, there's a 3% credit card fee on the amount funded by the credit card.