constant can be added in indexed mode and also immediate mode both depending on situation
No, Constant is Not added in immediate AM. In your original Question, You had asked "Adding register content to a Constant", For that I had said that "If this addition is done to get/fetch/manipulate the Data rather than Address, then that would mean "this Constant that you are adding, is itself an Operand. (i.e. Immediate AM)"
when register content added with constant value and stored in another register, then it will be indexed addressing mode?
No, when register content added with constant value and stored in another register, then it will be Two AMs, Register AM and Immediate AM.
You must be talking about this following example.
$ADD \,\,R_0,R_1, \,\,3000 \,\,\,\,|\,\,\, R_0\leftarrow M\left [R_1+3000 \right ]$ // Indexed AM
Here, We indeed are adding Register content with constant But we are Not storing that in another register directly. We are adding Register content with constant to get the address where the Operand is available.
See, Addressing Modes (Sticking to Data Centric AMs) only specify or giver information about the "Address" of the Operand/Data. One just can't see the Instruction and tell which AM has been used in that instruction Unless the specification/Working of that instruction has been given.
Is there any possibility that constant can be added with indirect or direct addressing mode too?
Unless one (Author/Manufacturer) defines these AMs in some other way, No, Conventionally We don't define these AMs where Constants are added to them in order to get the final Effective Address. But if you talk about "Possibility", Yes, Possibility is there Because Note that there is no generally accepted way of naming the various addressing modes. In particular, different authors and computer manufacturers may give different names to the same addressing mode, or the same names to different addressing modes. Furthermore, an addressing mode which, in one given architecture, is treated as a single addressing mode may represent functionality that, in another architecture, is covered by two or more addressing modes.
I don't want to Confuse anyone. Just Stick to the Conventional Use of Different AMs unless in GATE they "specify" it otherwise.