Assuming you entered that you would pay by check when you e-filed your original return, you don't need to remit payment. Because you intend to file by April 15th, what you are filing is technically a superseding return rather than an amended return, though you follow the same steps.
If you file the superseding return by mail, write "SUPERSEDING RETURN" across the top.
See here for more information from IRS about superseding returns.
See this older thread for more discussion of this issue.
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