how to find an amplitude value in frequency domain for a specific frequency while i'm having a CW signal in time domain?

hi guys. i created a signal CW in time domain with Gaussian noise. i need to to check what is the amplitude value in several specific frequencies? by doing FFT i do not get a good result, so i taught using the formula x[n]*e^(-i*2*pi*f*t), while f is a small vector of the specific frequencies which i need to check the amplitude values of them. i'll be more specific: i'm doing FFT to check the f_peak(which gives the maximum amplitude) and then i want to check by using the formula if there is any other frequency near by the f_peak(such as f_peak+0.001 Hz) which gives a better result for a maximum value in frequency domain. my question is how can i do that?

this is the code i wrote for building the CW signal in time domain and the code i wrote for finding the maximum value in FFT::

N=1500; Fs=10000; %frequency sample [sample per second] Ts=1/Fs; %Time sample [sec] time=(0:N-1)*Ts; %time vector [sec] x=0.707*sin(2*pi*4500*time); %sinusoid function in 4.5KHz frequency X=2*randn(size(x))+x; %sinusoid function plus AWGN

No=2^nextpow2(length(X)); %number of bins in the FFT (No=2048) zero_samp=No-length(time); %number of zero padding time=(0:No-1)*Ts; x_zero=[x zeros(1,zero_samp)]; %sinusoid function with ZERO PADDING

X_Zero=2*randn(size(x_zero))+x_zero; %sinusoid function plus AWGN with ZERO PADDING

%------------time domain------------

figure(1)

plot(1000*time,X_Zero)

xlabel('time [msec]')

ylabel('amplitude [volt]')

    Y=fft(X_Zero,No);
    Py=abs(Y)/No;
    f_resolution=Fs/No;
    f=0:f_resolution:Fs/2-1;                %vector frequencies of the possitive values
    Y_dB=20*log10(Py);                      %power dB
%-----------frequency domain--------
    figure(2)
    [Maximum,f_peak_index]=max(Y_dB);
    f_peak=f(f_peak_index);
    plot(1/1000*f,Y_dB(1:No/2))
    hold on
    xlabel('frequency [KHz]')
    ylabel('amplitude [dB]')
    plot(1/1000*f_peak,Maximum,'rx')