Hey @jh.koo this is working as intended. The Web3Modal only shows the option to connect with Metamask, if the Metamask is installed which is the case for PC. While on your phone, the Metamask might not be installed, that’s why it’s not showing the option.
The Metamask is not displayed when it’s on mobile device, because it checks whether it’s installed or not using injected scripts. When you connect Metamask on browser it kind of injects the script to listen to request and respond back. Since it’s installed on Mobile, you browser cannot communicate with the Mobile Application directly. In such cases you can use WalletConnect adapter. Or, you can open your website in the Metamask application browser it’ll work fine as you tested.
Can you please explain what do you mean by alerts if they don’t have a metamask?