The general idea of recursion is to have a terminating position that returns a constant value of some sort and then every other case is built on top of that.

For example, the factorial function, f(n) = n * (n-1) * (n-2) * ... * 2 * 1 has the following terminating condition and dependent functions:

f(1) = 1
f(n) = n * f(n-1) for all n > 1

so could be implemented as:

def factorial(n):
    if n == 1:
        return 1;
    return n * factorial(n-1)

In your particular case, the terminating condition is when either string is empty, at which point you just tack the other string onto the end. The dependent function is simply to grab the first character from the first string then call the next level down passing the rest of that string and the other string, but in reverse order so that you alternate.

def mix (s1, s2):
    if s1 == "" return s2
    if s2 == "" return s1
    return s1.firstChar() + mix (s2, s1.allButFirstChar());

In Java, this would translate to the following. Be warned that, if this is homework and you use this, you will almost certainly fail since you would be foolish to think your educators are not monitoring these sites.

public class Demo {
    public static String Mix (String s1, String s2) {
        if (s1.length() == 0) return s2;
        if (s2.length() == 0) return s1;
        return s1.substring(0,1) + Mix (s2, s1.substring(1));
    }
    public static void main(String[] args) {
        System.out.println (Mix ("Hello", "There"));
        System.out.println (Mix ("Hi", "There"));
        System.out.println (Mix ("Hello again", "Pax"));
        System.out.println (Mix ("", ""));
        System.out.println (Mix ("1111", ""));
        System.out.println (Mix ("111", "2"));
        System.out.println (Mix ("111", "22"));
        System.out.println (Mix ("111", "222"));
        System.out.println (Mix ("111", "2222"));
        System.out.println (Mix ("11", "2222"));
        System.out.println (Mix ("1", "2222"));
        System.out.println (Mix ("", "2222"));
    }
}

outputs:

HTehlelroe
HTihere
HPealxlo again

1111
1211
12121
121212
1212122
121222
12222
2222

This should work:

public String Interleave( String first, String second )
{
   if ( first.length() == 0 )
      return second;
   if ( second.length() == 0 )
      return first;
   return first.substring(0,1) + second.substring(0,1) +
      Interleave( first.substring(1), second.substring(1) );
}

This is the codingBat/String-2/mixString problem, except you want a recursive solution.

My solution is essentially the same as Kieveli s:

public String mixString(String a, String b) {
  return 
    a.isEmpty() ? b :
    b.isEmpty() ? a :
    a.substring(0, 1) + b.substring(0, 1)
      + mixString(a.substring(1), b.substring(1));
}

    String s1="12345";
    String s2="67890";


    char ch1[]  = s1.toCharArray();
    char ch2 [] = s2.toCharArray();

    char[] ch3 = new char[10];
   // System.out.println("ch1"+ch1);

    for(i=0;i<10;i++)
    {
        ch3[i*2]=ch1[i];

        ch3[i*2+1]=ch2[i];
        System.out.println("ttttttttttt");
         System.out.println(ch3[i]);
    }