PREREQUISITES

You must first understand how to create an item, which you can then turn into a spawn egg.

Spawn eggs are special items that, when used, spawn their corresponding mob. You can register one with the register method from your items class, by passing SpawnEggItem::new to it.

public static final SpawnEggItem CUSTOM_SPAWN_EGG = register(
		"custom_spawn_egg",
		SpawnEggItem::new,
		new Item.Properties().spawnEgg(EntityType.FROG)
);
	ItemGroupEvents.modifyEntriesEvent(CreativeModeTabs.SPAWN_EGGS)
			.register(itemGroup -> itemGroup.accept(ModItems.CUSTOM_SPAWN_EGG));

There are still a few things to do before it's ready: you must add a texture, an item model, a client item, a name, and add the spawn egg to the appropriate creative tab.

Adding a Texture

Create the 16x16 item texture in the assets/example-mod/textures/item directory, with the same file name as the id of the item: custom_spawn_egg.png. An example texture is provided below.

Download Texture

Adding a Model

Create the item model in the assets/example-mod/models/item directory, with the same file name as the id of the item: custom_spawn_egg.json.

{
  "parent": "minecraft:item/generated",
  "textures": {
    "layer0": "example-mod:item/custom_spawn_egg"
  }
}

Creating the Client Item

Create the client item JSON in the assets/example-mod/items directory, with the same file name as the id of the item model: custom_spawn_egg.json.

{
  "model": {
    "type": "minecraft:model",
    "model": "example-mod:item/custom_spawn_egg"
  }
}

Naming The Spawn Egg

To name the spawn egg, the translation key item.example-mod.custom_spawn_egg must be assigned a value. This process is similar to Naming The Item.

Create or edit JSON file at: src/main/resources/assets/example-mod/lang/en_us.json and put in the translation key, and its value:

{
  "item.example-mod.custom_spawn_egg": "Custom Spawn Egg"
}

Adding To A Creative Mode Tab

The spawn egg is added to the spawn egg CreativeModeTab in the initialize() method of the items class.

ItemGroupEvents.modifyEntriesEvent(CreativeModeTabs.SPAWN_EGGS)
		.register(itemGroup -> itemGroup.accept(ModItems.CUSTOM_SPAWN_EGG));

Check out Adding The Item To An Creative Mode Tab for more detailed information.