public class Aa extends Exception {

    public Aa(){
    }

    private String name;

    public String getName() {
        return name;
    }

    public void setName(String name) {
        this.name = name;
    }
}

public class C {

    private Exception e;

    public Exception getE() {
        return e;
    }

    public void setE(Exception e) {
        this.e = e;
    }

}

        Aa aa = new Aa();
        aa.setName("aa");
        C c = new C();
        c.setE(aa);
        String jsonC = JSON.toJSONString(c, SerializerFeature.WriteClassName);

        C c2 = JSON.parseObject(jsonC, C.class);
        System.out.println(c2.getE().getClass().getSimpleName());
        System.out.println(((Aa)c2.getE()).getName());