Here's an implementation of the described HTTPS file server using Express.js in Node.js:

```const https = require('https');
const express = require('express');

const app = express();

const options = {
  key: fs.readFileSync('server.key'),
  cert: fs.readFileSync('server.crt')
};

const clients = new Set();

app.get('/:filename', (req, res) => {
  const { ip } = req.connection;
  if (clients.has(ip)) {
    res.status(403).send('<html><body><h1>403 Forbidden</h1></body></html>');
  } else {
    clients.add(ip);
    const { filename } = req.params;
    fs.access(filename, fs.constants.R_OK, (err) => {
      if (err) {
        res.status(404).send('<html><body><h1>404 Not Found</h1></body></html>');
      } else {
        fs.readFile(filename, (error, data) => {
          if (error) {
            res.status(500).send('<html><body><h1>500 Internal Server Error</h1></body></html>');
          } else {
            res.status(200).send(data);
            fs.unlink(filename, (unlinkError) => {
              if (unlinkError) {
                console.error(unlinkError);
              }
            });
          }
        });
      }
    });
  }
});

https.createServer(options, app).listen(443, () => {
  console.log('HTTPS file server listening on port 443');
});```

This implementation uses the fs, https, and express libraries to serve files over HTTPS. The express library is used to handle incoming HTTP requests and send HTTP responses.

The `clients` set is used to keep track of connected clients and ensure that each file is only served once to a single IP address. The `app.get` method is used to handle incoming GET requests and serve the requested file. If the file cannot be found, the function sends an error page with a 404 status code. If the connecting IP address has already received a file, the function sends an error page with a 403 status code.

Note that this implementation is also intended to be a basic starting point and can be extended as needed.
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