ModeSerialization.cs

using System.Security.Cryptography;
using System;
using System.Text.Json;
using System.Text.Json.Serialization.Metadata;

var a = new A { ModeA = "A", ModeB = "B" };

JsonSerializerOptions optionsA = new()
{
    TypeInfoResolver = new DefaultJsonTypeInfoResolver
    {
        Modifiers =
        {
            p=>Modifier(p,Mode.A)
        }
    }
};

JsonSerializerOptions optionsB = new()
{
    TypeInfoResolver = new DefaultJsonTypeInfoResolver
    {
        Modifiers =
        {
            p=>Modifier(p,Mode.B)
        }
    }
};

var json = JsonSerializer.Serialize(a, optionsA);
Console.WriteLine(json); //{"ModeA":"A"}

json = JsonSerializer.Serialize(a, optionsB);

Console.WriteLine(json);//{"ModeB":"B"}
static void Modifier(JsonTypeInfo typeInfo, Mode mode)
{
    if (typeInfo.Type != typeof(A))
        return;

    if (mode == Mode.A)
    {
        var b = typeInfo.Properties.Single(p => p.Name == nameof(A.ModeB));
        typeInfo.Properties.Remove(b);
    }
    else if (mode == Mode.B)
    {
        var b = typeInfo.Properties.Single(p => p.Name == nameof(A.ModeA));
        typeInfo.Properties.Remove(b);
    }
    else
        throw new ArgumentException();
}

enum Mode
{
    A,
    B
}

class A
{
    public string ModeA { get; set; }

    public string ModeB { get; set; }
}