The units of mutual funds can neither be gifted nor transferred. The only situation in which a transfer is allowed from one person to another is upon the death of the investor. In such a situation, the nominee is required to produce the death certificate of the investor along with the KYC documents. The mutual fund units are then transmitted in the name of the nominee.
The only way out of gifting a mutual fund investment to someone, e.g., your children, is by making the investment in their own name. It is possible even if they are minors and haven't attained the age of 18. Either parent (father or mother) can act as the guardian for that purpose as minors are not allowed to make decisions related to redemption and purchase. Besides the birth certificate of the child, the fund house would need the KYC documents of the guardian. However, do note that income on selling mutual funds in the name of the minor child is clubbed to the income of the parent with higher income, for taxation purposes. But if the mutual fund investment is redeemed only after the child turns major (18-years old) it is taxed in the hand of the child only.
If you plan to gift a mutual fund investment (already in your name) to your child who has already attained the age of 18, there is no other way than redeeming your investment, transferring the proceeds to their bank account and asking them to make the investment afresh. Fund houses are not allowed to accept money from third parties - a person other than the one in whose name the units have to be issued. So the payment cannot be made directly from your bank account. But be mindful of capital gains tax while making such a transaction.