You say that you inherited the money from your mother, and are now paying these people using money that is already yours. Because of that, the money is considered a gift from you to them, and the fact that you are doing it in accordance with your mother's wishes doesn't change that. For it to be considered a bequest from your mother's estate directly to these beneficiaries, it would have had to be handled via the regular by-the-book inheritance procedure and been given to them directly rather than bequeathed to you with informal instructions to pass it on to them.
If one gives another person more than $14K in any calendar year, there is the potential gift tax issue to address. I'll explain why it's more a matter of 'addressing' than 'paying', as there are a number of legal ways around this.
Form 709 is what you'll use. In the end, you'll report the gifts over $14K but no tax will be due as they'll simply go against your lifetime gifting allowance, currently $5.49M per person.
Note, 2 ways to avoid even this obligation. If you have a spouse, you have a combined $28K/yr gifting (per recipient) with no reporting required. Similarly, if the recipient has a spouse, you can gift them $14K. i.e. couple to couple can gift $56K/yr. Last, why not just gift $14K before December, and in January, give the second installment? If I had money coming in separate from a will, I'd be happy that you honored a verbal request, and wouldn't be so greedy as to expect you to risk a dime of your own finances to transfer the funds immediately.