I would like to add "Like" feature in Modern pages using SPFx or any other way. Please help.
Is it possible to use reputation feature for this like SP 2013?
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You can design an application customizer and display a "Like" control on top or bottom of each page.
Once a user clicks your custom button, call external API and save vote in your database.
The reputation feature is in the community site. If you want to use reputation feature, you should create the community site.
If you want to use “Like” feature, you could go to page library->library settings-> Rating settings->enable Like feature. It will display “Like” button in the page library.
And if you want to add the Like button in the modern page by spfx solution, you could develop the custom code.