How to generate serialVersionUID for kotlin exceptions?

Yes, you can declare it in the companion object. The doc says:

Also, public properties defined in objects and companion objects, as well as top-level properties annotated with const, are turned into static fields in Java

But that seems to be the case with private properties too:

class MyException: Exception() {
    companion object {
        private val serialVersionUid: Long = 1
    }
}

javap -c -p com.ninja_squad.kotlindiscovery.MyException.class

Compiled from "MyException.kt"
public final class com.ninja_squad.kotlindiscovery.MyException extends java.lang.Exception {
  private static final long serialVersionUid;

  public static final com.ninja_squad.kotlindiscovery.MyException$Companion Companion;

  static {};
    Code:
       0: getstatic     #38                 // Field com/ninja_squad/kotlindiscovery/MyException$Companion.INSTANCE:Lcom/ninja_squad/kotlindiscovery/MyException$Companion;
       3: putstatic     #40                 // Field Companion:Lcom/ninja_squad/kotlindiscovery/MyException$Companion;
       6: lconst_1      
       7: putstatic     #21                 // Field serialVersionUid:J
      10: return        

  public com.ninja_squad.kotlindiscovery.MyException();
    Code:
       0: aload_0       
       1: invokespecial #15                 // Method java/lang/Exception."<init>":()V
       4: return        

  public static final long access$getSerialVersionUid$cp();
    Code:
       0: getstatic     #21                 // Field serialVersionUid:J
       3: lreturn       
}

To create the serialVersionUID for a class in Kotlin you have a few options all involving adding a member to the companion object of the class.

The most concise bytecode comes from a private const val which will become a private static variable on the containing class, in this case MySpecialCase:

class MySpecialCase : Serializable {
    companion object {
        private const val serialVersionUID: Long = 123
    }
}

You can also use these forms, each with a side effect of having getter/setter methods which are not necessary for serialization...

class MySpecialCase : Serializable {
    companion object {
        private val serialVersionUID: Long = 123
    }
}

This creates the static field but also creates a getter as well getSerialVersionUID on the companion object which is unnecessary.

class MySpecialCase : Serializable {
    companion object {
        @JvmStatic private val serialVersionUID: Long = 123
    }
}  

This creates the static field but also creates a static getter as well getSerialVersionUID on the containing class MySpecialCase which is unnecessary.

But all work as a method of adding the serialVersionUID to a Serializable class.

You can use this plugin GenerateSerialVersionUID to automatically generate the serialVersionUID field.

Since Kotlin language does not support static, you need to use the const decoration in the generated companion object (of course, it is also possible to use the @JvmField annotation).