Let me know if there is a better way to do this. I was thinking of using some kind of a sorted map instead of iterating through the entrySet and storing the highest values, but I did not find relevant information regarding this.
package com.codegym.task.task18.task1823;

import java.io.*;
import java.security.KeyStore;
import java.util.*;

/*
Threads and bytes

*/

public class Solution {
    public static Map<String, Integer> resultMap = new HashMap<String, Integer>();

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        //read filenames from the console until the word "exit" is entered
        //pass the filename to the readthread thread
        //the thread should find the byte (so the element, not how many times it occurs)
        //that occurs most frequently in the file and add it to
        //the resultMap where the String parameter is the fileName and the Integer parameter is
        //the relevant byte.

        while (true){
            String fileName = br.readLine();
            if (fileName.equals("exit")) {
                br.close();
                break;
            }
            ReadThread readThread = new ReadThread(fileName);
            readThread.start();
        }
    }

    public static class ReadThread extends Thread {
        String fileName;
        public ReadThread(String fileName) throws FileNotFoundException {
            // Implement constructor body
            this.fileName = fileName;

        }
        public void run(){
        // Implement file reading here
            //I have created a map in which I will add all of the elements from the file
            //and the number of times they are found
            HashMap<Integer, Integer> sortedMap = new HashMap<>();
            try {
                FileInputStream fileInputStream = new FileInputStream(fileName);
                //here I am reading the bytes from the file
                while (fileInputStream.available()>0){
                    int byteRead = fileInputStream.read();
                    //the condition below checks if the file is present and increments value
                    //or adds the key to the map and value 1 because it is the 1st time it shows up
                    if (sortedMap.containsKey(byteRead)){
                        sortedMap.replace(byteRead, sortedMap.get(byteRead) + 1);
                    } else sortedMap.put(byteRead, 1);
                }
                //here I declare a value and key which will store value and key when I iterate
                //through the map
                int value = Integer.MIN_VALUE;
                int key = 0;
                //declaring the entry set -a clone- of the sortedMap
                Set<Map.Entry<Integer,Integer>> entries = sortedMap.entrySet();
                //iterating through the clone
                for(Map.Entry<Integer,Integer> entry:entries) {
                    if(entry.getValue() >= value) {
                        value = entry.getValue();
                        key = entry.getKey();
                    }
                }
                resultMap.put(fileName, key);
                fileInputStream.close();

            } catch (FileNotFoundException e) {
                e.printStackTrace();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
}