Ya he tenido vs Ya he habido

Ya he tenido vs Ya he habido
 

¡Ya he habido suficiente de esta tonterías!
¡Ya he tenido suficiente de esta tonterías!

Como siempre, gracias.

You wont hear he habido used much in this manner. You would more likely hear ha habido (there has occurred) Also it would be estas tonerías

tener = have (possess)
haber = have (auxiliary verb, used to form the perfect tenses, always followed by a (past) participle)

Perfect Present Tense
he hablado = I have spoken
has comido = you have eaten
han vivido = they have lived
he tenido = I have had

ha habido = There has/have been/occurred/existed (Don't use 'han habido' in an impersonal sense.)

'He habido' is rarely used, but does exist. Most native speakers would argue that it doesn't exist, because it's hard to think of any sentence where it would make sense. It'd be better to avoid using any of the personal conjugations, and stick to only the impersonal 'ha habido', as poli stated.
The verbal periphrasis haber de + infinitivo exists, and can be used as a personal verb, where the action expressed by the infinitive describes an obligation, convenience/advantage, or necessity for the person. It means the same thing as 'tener que + infinitivo', which is preferred over 'haber de + infinitivo'.
While 'haber de + infinitivo' can be used in a personal way, 'haber que + infinitivo' is only used impersonally (only conjugated in the third-person singular form); i.e., hay que saber.

Así que "He tenido......" ¿Es correcto y yo debería de olvidar del otro?

Como siempre, gracias.

Sí, si quieres decir "I've had."