Correct way to set normal strength
Assuming that the normal was created by differentiating some height field f(u,v):

N = normalize(df_du, df_dv, 1)


What you probably want to achieve is to "strengthen" your normals as-if by scaling that height field by a factor C:

g(u,v) = C*f(u,v)


Then your new normal would be:

M = normalize(dg_du, dg_dv, 1) = normalize(C*N0, C*N1, N2)


Translating that to GLSL in your shader:

vec3 GetNormal(){
    vec3 n = texture(normalMap,uv).xyz;
    n = n * 2.0 - 1.0;
    n.xy *= C;
    n = normalize(n);
    return  normalize (v_TBN * n);
}


By constructing a normal map texture that stores only the height-field gradient (df_du, df_dv) without normalization, using the internal format GL_RG8_SNORM for the texture, and making sure that v_TBN is orthonormal, you can simplify it further to:

vec3 GetNormal() {
    vec3 n = normalize(vec3(texture(normalMap,uv).xy, C));
    return v_TBN*n;
}