Doubt regarding on excitation of TE10,TM10,TE01,TM01 modes in waveguides

Dear Sir,
Whenever we are transmitting the signals through the waveguide, we are calling as TE₁₀mode without any excitation. My doubt is, how it is exciting for TE₁₀ mode without any excitation

I have the following doubts on the excitation

(1) How we can excitation the TE₀₁, TE₁₁,TE₀₀. Similarly how we can excitation TM₀₁,TM₁₁,TM₀₀.

(2) Do we need to connect antenna or something else to get excitation of particular mode.

(3) Which is the best mode for transmitting signals through the waveguide either TE mode and TM mode. For TE mode, which is the best mode and for TM mode, which is the best mode.

From your questions I an see that what you need is the basic knowledge of the basic waveguide handbook.
The TE10 mode is the dominant mode in a rectangular waveguide. To excite it there are several coaxial-to-waveguide transitions, each design corresponds to a low loss, wide bandwidth, high power, etc.
Other modes can be excited by similar transitions, using either probes (E components) or loops (H-components). Certain modes have advantages in building various devices (couplers, filters). Higher modes find a use in "overmode" waveguides like optical feed structures for antennas.
Go to a library and read books on waveguides and applications.

Dear Sir,
I agree with you, TE10 mode is dominant mode in rectangular waveguide. But we are not using anything to excitation for getting TE10 mode, we are calling as TE10 mode. How it is possible for getting TE10 mode without excitation that is my doubt. Similarly for other modes of TE and TM , how we have to get the excitation

May be you reading something into the term "excitation" that it doesn't mean.

It simply means that you are feeding a high frequent signal to the waveguide and it propagates therein as an electromagnetic wave of a specific form or "mode". The wave mode is commanded by the field pattern of the transition (capacitive or inductive coupler, position and orientation in the waveguide). Also a transition between two waveguides can cause a mode change.

In any case, there won't be TE00 or TM00 modes in a waveguide.

I support the "book" suggestion.

It may be possible you do not understand what "excitation" means. It means you feed energy into a waveguide to create the desired mode, e.g. TE10. The energy must be fed at a proper frequency and E=component vector at waveguide center aligned with the longer cross=section axis.
Books show a variety of devices to excite desired modes in waveguides. Start reading .

The other way to excite TE10 mode in a waveguide is by connecting a horn antenna to it.