I know an exchange that can do that for you but for that you'll have to download an open-source wallet software like Electrum and then create your own personal wallet on that wallet software. Once your wallet is created then you'll have to save your seed words and private keys.

Never share the private keys and seed phrase with anyone and write those on a paper as well as save those on a SSD and then copy your wallet address and disable the internet on the computer where you have installed your wallet software and never connect it on internet again. You'll only need that wallet address that you have generated and other than that you don't need anything else.

Now you can use any centralized exchange or decentralized exchange to buy Bitcoin and once you have bought the Bitcoin then withdraw those Bitcoin into the wallet address that you have copied. You can do that every month by buying Bitcoin on those online exchanges and withdrawing those Bitcoin into your own personal wallet that I referred as an exchange in order to make your Bitcoin secure.

That's the most secure way to buy and store Bitcoin and you'll never have to worry about any theft or any other issue as long as you don't use your seed phrase or private key on any other computer. The moral of this post is to never trust the exchanges that have control over your keys because if the keys are not yours then the coins aren't yours. In Bitcoin investment trusting anyone can be dangerous and trusting online wallets is the stupidest thing that anyone can do.