Students' ability to assess their own knowledge is an important skill in science education. However, students often overestimate their actual performances. In such cases, overconfidence bias arises. Previous studies in physics education have shown that overconfidence bias concerns mainly content areas, such as Newtonian mechanics, where misconceptions are strongly held by students. However, how the received instruction and the levels of understanding of a given topic influence overconfidence bias is yet to be proved. In this paper, we address this issue choosing as content area introductory quantum mechanics (QM). Overall, 408 high school students were involved in the study and randomly assigned to two experimental groups. One group received a textbook-based instruction about introductory QM, whereas the other one received instruction on the same topics through an innovative guided inquiry teaching-learning sequence (TLS), which included also potential pedagogical countermeasures for overconfidence bias. Students of both experimental groups completed a multiple-choice questionnaire and indicated for each item the degree of their confidence in the given answer using a 5-point Likert scale. The overconfidence bias was quantitatively defined and evaluated at person level using a 1D Rasch model. Progress in knowledge about the targeted topics was modeled according to a construct map validated in a previous paper. Results show that, for the whole sample, the overconfidence bias decreased as students progressed along the levels of the construct map. However, findings indicate that students of the TLS group achieved a significantly higher accuracy and a better confidence calibration, while the textbook group exhibited a lower performance and a significantly greater overconfidence bias. Implications for research into overconfidence bias in physics education are briefly discussed.