Gemora Avoda Zarah Daf 8a
Said Rab Judah the son of Samuel b. Shilath in the name of Rab: Even
though it was said that one should pray for his private needs only at
‘Who heareth prayer,’ nevertheless, if he is disposed to supplement
any of the Benedictions [by personal supplications] relevant to the
subject of each particular Benediction, he may do so. [So also] said
R. Hiyya b. Ashi in the name of Rab: Even though it has been said that
one should pray for his own needs only at ‘Who hearest prayer’, still
if [for example] one has a sick person at home, he may offer [an
extempore] prayer at the Benediction for the Sick or if he is in want
of sustenance, he may offer a [special] prayer in connection with the
Benediction for [Prosperous] Years.
For a specific request that is within the realm of one of the brachot that have the same theme ( i.e asking for livelihood during birkat hashanim) than that is the correct place to ask.
However for general requests, Shomea Tefila seems to be the appropriate place.
ברכה שומע תפילה הינה ברכה אישית, וניתן לומר בקשות אישיות באמצע הברכה. כך נפסק להלכה בשולחן ערוך, על פי התלמוד: "שואל אדם צרכיו ב'שומע תפילה'".
Wiki Shomea Tefila (hebrew)